Chapter 13 Exercise 13.1
|
|
- Ethan Lester
- 5 years ago
- Views:
Transcription
1 Chapter 1 Exercise 1.1 Q. 1. Q.. Q.. Q. 4. Q.. x x 1 (x + 1) + 4x + (x 1) + 9x 4x + + 9x 1x 1 p p + (p ) p 1 (p + ) + p 4 p 1 p 4 p 19 y 4 4 y (y 4) 4(y ) 1 y 1 8y + 1 y y 1 + y y + y y x x x x + 14 (x + 1) 14() + 1(x + ) 14 4x x + _ 14 x 4 14 Q.. Q q 1 1 7q + 4(4q ) 1 (7q ) (4q ) (7q ) q 8 14q q 1 q 1 x 1 x 4 (x 1) (x 4) x x x Q. 8. r 4r + Q. 9. Q.. r r 1 1 4r + r 1r 1 1() 1 (4r + ) 1 1r 4 1r 9 r 1 r 4 1 x 9 x 9 x x ( x) x 1 x 9 ( x). x x 9 + x x x 19 1 x + x. 1 x +. x x + 1 x 17 x (r) 1 Active Maths (Strands 1 ): Ch 1 Solutions 1
2 Q. 11. Q. 1. Q. 1. Q. 14. Q. 1 Q. 1. Q x x. 1 x x x x x x 8 x x x + 4 x _ 8. x 1. (x + 1) (x + 1). x 8x x 1 (x + 1)x 7x 1 (x + 1)x. x (x + 4) (x + 4). x x x 8 (x + 4)x x 8 (x + 4)x x 1 + x 1 _ (x 1) + (x 1) (x 1)(x 1) 19x 7 (x 1)(x 1) 1 x + 4x 1(4x ) (x + )(4x ) (x + ) (x + )(4x ) 4x x 1 (x + )(4x ) x 17 (x + )(4x ) 1 x x 1(7 x) + (x + 1) (x + 1)(7 x) _ 7 x + x + (x + 1)(7 x) 9x + 9 (x + 1)(7 x) x 1 4x _ (4x ) (x 1) (x 1)(4x ) 1x 9 x + (x 1)(4x ) x 4 (x 1)(4x ) Q. 18. Q. 19. Q.. Q. 1. Q.. x + x + (x + ) + ( x) ( x)(x + ) x x ( x)(x + ) 4x + ( x)(x + ) x x (x ) (x ) (x )(x ) x 4x + (x )(x ) x (x )(x ) 11 x + x 11x + x 4 (x )( x) 18 9x (x )( x) 9( x) (x )( x) 9 x OR 11 x + x 11 x x 11 x 9 x x x x x 4 4 x 4 7 x + x 7 x x x 11( x) + (x ) (x )( x) Active Maths (Strands 1 ): Ch 1 Solutions
3 Q.. (i) 1 x x Q. 4. (i) x x + 4 1(x + 4) (x) x. (x + 4) x + 4 x x(x + 4) x + 4 x(x + 4) (iii) Let x x + 4 x(x + 4) + 4 (() + 4) + 4 (4 + 4) Let x (iv) The answers to parts (i) and (iii) are the same. x 1 + Let x x + 4 ( ) 1 + ( ) ( ) (11) 18 4 x 1 + x + 4 _ (x + 4) + (x 1) (x 1)(x + 4) x x (x 1)(x + 4) x + (x 1)(x + 4) (x + 1) (x 1)(x + 4) (iii) Let x (x + 1) (x 1)(x + 4) ( + 1) (. 1)(. + 4) Q.. 4 (i) x + 8 x Let x 1 4 x + 8 x 4 ( 1_ ) + 8 1_ 4 1_ + 8 1_ 4 1_ _ 4_ x + 8 x 4(x ) + 8(x ) (x )(x ) 4x 1 + 4x 1 (x )(x ) 44x 8 (x )(x ) Active Maths (Strands 1 ): Ch 1 Solutions
4 Q.. (i) (iii) Let x 1 44 ( 1_ ) 8 (( 1_ ) ) ( 1_ ) 8 ( 1_ )( 1_ ) + 1_ _ 1 _ x x + 1_ _ x x + (x + ) + (x + 1) (x + 1)(x + ) x + + x + (x + 1)(x + ) 1x + 1 (x + 1)(x + ) (iii) Let x 1 1 ( 1_ ) + 1 ( 1_ + 1 )( 1_ + ) _ Exercise 1. Q. 1. Q.. Q.. Q. 4. Q.. Q.. Q. 7. Q. 8. Q. 9. Q.. Q. 11. Q. 1. Q. 1. Q. 14. Q. 1. Q. 1. (x + 1)(x ) (x ) (x + 1) (x + 4)(x + ) (x + 4)(x + ) x + (x + ) (x + 4) x + 4 x + x + (x + ) (x + ) 4x + (x + 1) (x + 1) x + 1 x 1 x 1 (x + 1) 18y 4 y x 1 x 4 x x x 4x 4 x 4 (x 1) (x 1) 1 (x + ) x + (9y ) (y 1) 9y y 1 (x 4)(x + 4) (x 4) (x + 4) x + 4 x (x ) x (x ) (x 8)(x + 8) (x 4) (x 4)(x + 8) (x 4) (x + 8) 4x + 1 or 4(x + 4) y 1 1 y 1(1 y) 1 (1 y) x + x + 8 (x + 4)(x + ) x + 4 (x + 4) x + 4 8p q pq 8. p. p. p. q. q. p. q. q a bc ac 4p a a b c a c c ab c x x (x + )(x ) x x + x + 18p q r 18. p. p. p. q. q. r. r p 4 q r p. p. p. p. q. q. r 18. r p 4 Active Maths (Strands 1 ): Ch 1 Solutions
5 Q. 17. Q. 18. Q. 19. a + 4a (a + a ) a + a 1x + 18x x x _ x(x + x ) x x + x 4x + 7x (x + )(4x 1) x + (x + ) 4x 1 Q.. (i) x x + 1 (x 7)(x ) (x )(x x + 1) x x + 1x x + x x 1x + 71x (iii) x 1x + 71x x (x )(x 7)(x ) (x ) (x )(x 7) Q.. 9x x (x + 1)(x ) x + 1 (x + 1) x Q. 1. (i) 1x 1 1(x 1) 1(x 1)(x + 1) (x + 1)(x + 1) (iii) 1x 1 x + x + 1 1(x 1)(x + 1) (x + 1)(x + 1) 1(x 1) x + 1 Q.. (i) x + 9x + (x + )(x + 4) (x + 1)(x + 9x + ) x + 9x + x + x + 9x + x + x + 9x + _ (iii) x + x + 9x + (x + 4) _ (x + 1)(x + 9x + ) (x + 4) (x + 1). (x + ). (x + 4) (x + 4) (x + 1)(x + ) (iv) Let x Solution ( + 1)( + ) 7 1 _ x + x + 9x + x ( ) + 9() (iv) Let x 4: (4 )(4 7) ( 1)( ) x 4: 4 1(4 ) + 71(4) Q. 4. (i) x 17x (x + 1)(x ) 1(x 17x ) x(x 17x ) x 17x x + 17x + x Q.. Q.. Q. 7. Q. 8. x + x 11x _ (1 x)(x + 1)(x ) (iii) x + 1 (1 x)(x ) (iv) ( 1) + ( 1) 11( 1) ( 1) (1 + 1)( 1 ) 14 (x + 1)(x + ) (x + )(x 4) x + 1 x 4 x + 9x + 4 x + 11x + (x + 1)(x + 4) (x + 1)(x + ) x + 4 x + x 8x 1 x x 4(x x ) (x x ) 4 ax + ay cx cy ax + ay + cx + cy a(x + y) c(x + y) a(x + y) + c(x + y) (x + y)(a c) (x + y)(a + c) a c a + c Active Maths (Strands 1 ): Ch 1 Solutions
6 Q. 9. Q.. (x x 1) 4(x + 1x + 1) (x + 4)(x ) (x + 4)(x + ) x (x + ) a b b a (a b) (b a)(b + a) 1. (b a) (b a)(b + a) 1 b + a Exercise 1. Q. 1. (i) x + 7x + 1 (x + 4)(x + ) x + 7x + 1 (x + 4)(x + ) x + (x + ) x + 4 (iii) x + 4 x + x + 7x + 1 x + x 4x + 1 Answer: x + 4 4x + 1 Q.. (i) x + 11x + (x + 1)(x + ) x + 11x + (x + 1)(x + ) x + (x + ) x + 1 (iii) x + 1 x + x + 11x + x + x x + x + (iii) x + 7 x 9 x x x 9x 7x x Answer: x + 7 7x Q. 4. (i) x 7x (x + 4)(x ) Q.. Q.. x 7x (x + 4)(x ) x (x ) x + 4 (iii) x + 4 x x 7x x 1x 8x x Answer: x + 4 8x 4 x 8x 8x + 1 8x 4x 4x x + 1 Answer: 8x 4 4x + 1 x 7 x + x 11x x + x Answer: x 7 1x 1 1x 1 8x Answer: x + 1 Q.. (i) x x (x 9)(x + 7) x x (x 9)(x + 7) x 9 (x 9) x + 7 Active Maths (Strands 1 ): Ch 1 Solutions
7 Q. 7. x + x + 1 x + x + x + 7x + x + x x + 7x x + x Answer: x + x + 1 x + x + Q. 8. x + 4x + 1 x x + x 7x x x 4x 7x 4x 8x Answer: x + 4x + 1 Q. 9. x + x + 1 x + 8x + x + x x + Answer: x + x + x x Q.. 8x x + 1x + 14x 1 1x + 4x Answer: 8x x 1 x 11 Q. 11. x + x 8 x + 9 x + 1x + x 7 x + 9x 4x + x 4x + 18x 1x 7 1x 7 Answer: x + x 8 Q. 1. x 8x x x x x + 1 Q. 1. Q. 14. x + x Answer: x 8x 4x x x +1x 18x x + 1 x + x + x + 1 4x + x + 8x + 4x + x 4x + 8x Active Maths (Strands 1 ): Ch 1 Solutions 4x + x x + Answer: x + x + x + 7x + 4x x + 14x + 4x + 1x 14x + x 8xx + 1x 8x + x 4x x +4x + Answer: 7x + 4x Q. 1. x x + 8 7x x 1x + 74x 48 x x 1x + 74x Answer: x x + 8 1x + 18x x 48 x 48 7
8 Q. 1. x 8x 8 x 1 x 9x + 8 x x 8x + x 8x + 8x 8x x Answer: x 8x 8 Q. 17. x x + x 4 x + x x 4 x 4 Answer: x Q. 18. x + x 4x 4x x x x Answer: x + x Q. 19. x + x x 1 9x 19x + 9x + x x 19x + x + x 18x x + Answer: x + x Q.. (i) (x + )(x 7) x x 14 (x 1)(x x 14) x x 8x x + x + 14 x 11x x + 14 (iii) x 11x x + 14 x 7 (iv) x x 14 x 1x 11x x + 14 x x x x x + x Answer: x x 14 (x 1)(x x 14) (x 7) _ (x 1)(x + )(x 7) (x 7) (x 1)(x + ) 8x x + 14 Q. 1. (i) (x + )(x 4) x x 1 (x 1)(x x 1) x 1x x x + x + 1 x 17x 1x + 1 (iii) x 17x 1x + 1 x + (x 1)(x x 1) (x + ) (x 1)(x + )(x 4) (x + ) (x 1)(x 4) 8 Active Maths (Strands 1 ): Ch 1 Solutions
9 (iv) x x 1 x 1 x 17x 1x + 1 x x 1x 1x 1x + x x + 1 x + 1 Answer: x x 1 Q.. x + x 1 x + 1 x + x x 1 x + x x x x + x 4x 1 4x 1 Answer: x + x 1 (x + 4)(x ) Q.. x x 1 x + 1 x 1x 1 x + x x 1x x x 1x x 1 1x 11 Q. 4. k + 7k k k + 9k k + k k 14k k 14k k k k + k + Answer: k + 7k Let k k + 7k + 7() k + 9k k + () + 9() () Answer: x x 1 (x 4)(x + ) Q.. (i) 4a + a 7 a + a + 9 a 4a + a + a 7 (4a + a ) 1a + a (1a + 18a) 18a 7 18a 7 Answer: a + a + 19 Active Maths (Strands 1 ): Ch 1 Solutions 9
10 Q.. (i) x 1 (x 1)(x + 1) 4x 7x + (4x )(x 1) (iii) (x + 1)(4x 7x + ) 4x 7x + x + 4x 7x + 4x x 4x + (iv) 4x x 4x + x 1 _ (x + 1)(4x 7x + ) (x + 1)(x 1) 4x 7x + (4x )(x 1) x 1 (x 1) 4x Q. 7. 8x 1 x 1 4x + x + 1 x 18x + x + x 1 8x 4x 4x + x 4x x x x 11 Answer: 4x + x + 1 x 1 Q. 8. 9x 1x + 1 x + 4 7x + x + x + 4 7x + x x + x x 48x 48x x + 4 Answer: 9x 1x + 1 Revision Exercises Q. 1. (a) (i) x + 1 x + x x + 48x + 4 (x + 1) + (x + ) x + + x + 1 x + 17 x 1 + x + 7 7x 7 + x + 7 9x + 7 Active Maths (Strands 1 ): Ch 1 Solutions
11 (iii) x 1 (iv) 7x (b) (i) a a 1 a + b a + b x 1 x 1 (x 1) (x 1) 1x x + 1x 1 + x + (a + b) (a + b) (iii) x 4 x 4 (x ) (x )(x + ) x + (c) (i) x + x + x + 1x + x + x x x + x + Answer: x + 4a + a + 1a + 14a + 4 1a + 8a a a + 4 Answer: 4a + a + 4 (iii) c + 7 c 1c + 11c 14 1c c 1c c 14 Answer: c + 7 1c 14 (x )(x + 4) Q.. (a) (i) x (x + 4) 4(x + 1) 4 (x + 1) 7x (x 1) + (x + ) 7x 4x + + x + 1 8x + 1 Active Maths (Strands 1 ): Ch 1 Solutions 11
12 (iii) x + x 1 (x + )(x ) x x + (x + ) (iv) 4a b ab (v) x x x + 1 (b) (i) x 1 (iii) 4 a. a. b. b. b. a. b x 4 x + x 1 4 x 7 x ab (x )(x + 1) x (x + 1) + x + (x 1) 1(x 4) + (x + ) 1x 4x + + x + x + 4 (x 1) + (x ) (x )(x 1) 9x + x (x )(x 1) 11x 1 (x )(x 1) _ 4( x) 7(x ) (x )( x) x (x )( x) 11(. x) (x )( x) 11 x (c) (i) x + 1x + (x + 8x + 1) (x + 4)(x + 4) Q.. (a) (i) x + 1x + (x + 4)(x + 4) (x + 4) (x + 4) (iii) x + 1x + (x + 4) () + 1() + 81 x 4x 1 (x ) (x ) 1 x 9 x 4x + (x )(x + ) (x )(x 1) x + x 1 (iii) x 7x + (x )(x 1) x 1 (x ) x 1 (iv) x + x 8 (x 7)(x + 4) x + 8 (x + 4) x 7 1 Active Maths (Strands 1 ): Ch 1 Solutions
13 (b) (i) x + 7x 4 (x 1)(x + 4) x 1 x + 4 (x + 4) x + 7x x x + 9x x + x x 14x x 14x x x + x + Answer: x + 7x (iii) x x + 1 x + x 14x 9x + x + 4x 18x 9x 18x 1x x x + x + Answer: x x + 1 (iv) 4x + x + x 1 8x + x 8x 4x 4x + x Answer: 4x + x + 4x x x x (c) 8 x 1 x 8 x + 1 x x Let x 9 Solution Using x 1 x Same Active Maths (Strands 1 ): Ch 1 Solutions 1
14 Q. 4. (a) (i) x x 4x 1x + 9 4x x x + 9 x + 9 So 4x 1x + 9 x x x + 4x 4x 11x + 1x 1x + 1x x 1x 1x 1x 4x 1x x + 1x + So 1x + 1x 1x + x 4x 1 + 4x (iii) x + x + x x 19x x x x 19x x x x x So x 19x x x + x + (iv) x + x + 1 x 1 xx + 8x 1 x + x 9xx 1 Answer: x + x + 1 9x + x x x 1 x + 1 (b) (i) x x x x 1 11 x 1 x + x + x (x + ) (x + )(x 1) 1 x 1 14 Active Maths (Strands 1 ): Ch 1 Solutions
15 (iii) x x + x + x + x 11 x 1 + (x + ) (x 1)(x + ) 11 x x 1 1 x 1 Q.. (i) Divisor Quotient Dividend x 1 x x 1x + 4x 1 x + 1 8x + x 1 x 1 x x 4 x 4x x + 4 x x x + 4 1x 4x + 17x 1 x x 4 x 1 x 4x x + 4 x + x x x x + x 4x x + 4 (x )(x x + 4) x(x x + 4) (x x + 4) 1x x + 8x 18x + 9x 1 1x 4x + 17x 1 x + x 1 x + x 48x 8 x 48x x + 48x 48x 8 Division: x + p q x 8 Active Maths (Strands 1 ): Ch 1 Solutions 1
Math 101, Basic Algebra Author: Debra Griffin
Math 101, Basic Algebra Author: Debra Griffin Name Chapter 5 Factoring 5.1 Greatest Common Factor 2 GCF, factoring GCF, factoring common binomial factor 5.2 Factor by Grouping 5 5.3 Factoring Trinomials
More informationChapter 4 Partial Fractions
Chapter 4 8 Partial Fraction Chapter 4 Partial Fractions 4. Introduction: A fraction is a symbol indicating the division of integers. For example,, are fractions and are called Common 9 Fraction. The dividend
More information1.4. Arithmetic of Algebraic Fractions. Introduction. Prerequisites. Learning Outcomes
Arithmetic of Algebraic Fractions 1.4 Introduction Just as one whole number divided by another is called a numerical fraction, so one algebraic expression divided by another is known as an algebraic fraction.
More informationSection 5.3 Practice Exercises Vocabulary and Key Concepts
Section 5.3 Practice Exercises Vocabulary and Key Concepts 1. a. To multiply 2(4x 5), apply the property. b. The conjugate of 4x + 7 is. c. When two conjugates are multiplied the resulting binomial is
More information4x + 5y 5 If x = 0 find the value of: (substitute) 13 (x 2)(x + 5) Solve (using guess and check) 14
Algebra Skills MCAT preparation # DO NOT USE A CALCULATOR 0z yz (x y) Expand -x(ax b) (a b) (a b) (a b)(a b) (a b) x y + abc ab c a bc x + x + 0 x x x = 0 and y = - find the value of: x y x = and y = -
More informationMath 154 :: Elementary Algebra
Math 1 :: Elementar Algebra Section.1 Exponents Section. Negative Exponents Section. Polnomials Section. Addition and Subtraction of Polnomials Section. Multiplication of Polnomials Section. Division of
More informationMath1090 Midterm 2 Review Sections , Solve the system of linear equations using Gauss-Jordan elimination.
Math1090 Midterm 2 Review Sections 2.1-2.5, 3.1-3.3 1. Solve the system of linear equations using Gauss-Jordan elimination. 5x+20y 15z = 155 (a) 2x 7y+13z=85 3x+14y +6z= 43 x+z= 2 (b) x= 6 y+z=11 x y+
More informationFactoring Methods. Example 1: 2x * x + 2 * 1 2(x + 1)
Factoring Methods When you are trying to factor a polynomial, there are three general steps you want to follow: 1. See if there is a Greatest Common Factor 2. See if you can Factor by Grouping 3. See if
More informationName. 5. Simplify. a) (6x)(2x 2 ) b) (5pq 2 )( 4p 2 q 2 ) c) (3ab)( 2ab 2 )(2a 3 ) d) ( 6x 2 yz)( 5y 3 z)
3.1 Polynomials MATHPOWER TM 10, Ontario Edition, pp. 128 133 To add polynomials, collect like terms. To subtract a polynomial, add its opposite. To multiply monomials, multiply the numerical coefficients.
More informationMath Final Examination STUDY GUIDE Fall Name Score TOTAL Final Grade
Math 10006 Final Examination STUDY GUIDE Fall 010 Name Score TOTAL Final Grade The Use of a calculator is permitted on this exam. Duration of the test is 13 minutes and will have less number of questions
More informationMath 234 Spring 2013 Exam 1 Version 1 Solutions
Math 234 Spring 203 Exam Version Solutions Monday, February, 203 () Find (a) lim(x 2 3x 4)/(x 2 6) x 4 (b) lim x 3 5x 2 + 4 x (c) lim x + (x2 3x + 2)/(4 3x 2 ) (a) Observe first that if we simply plug
More informationMultiplication of Polynomials
Multiplication of Polynomials In multiplying polynomials, we need to consider the following cases: Case 1: Monomial times Polynomial In this case, you can use the distributive property and laws of exponents
More informationDownloaded from
9. Algebraic Expressions and Identities Q 1 Using identity (x - a) (x + a) = x 2 a 2 find 6 2 5 2. Q 2 Find the product of (7x 4y) and (3x - 7y). Q 3 Using suitable identity find (a + 3)(a + 2). Q 4 Using
More informationTopic 12 Factorisation
Topic 12 Factorisation 1. How to find the greatest common factors of an algebraic expression. Definition: A factor of a number is an integer that divides the number exactly. So for example, the factors
More informationDivision of Polynomials
Division of Polnomials Dividing Monomials: To divide monomials we must draw upon our knowledge of fractions as well as eponent rules. 1 Eample: Divide. Solution: It will help to separate the coefficients
More informationa*(variable) 2 + b*(variable) + c
CH. 8. Factoring polynomials of the form: a*(variable) + b*(variable) + c Factor: 6x + 11x + 4 STEP 1: Is there a GCF of all terms? NO STEP : How many terms are there? Is it of degree? YES * Is it in the
More informationSandringham School Sixth Form. AS Maths. Bridging the gap
Sandringham School Sixth Form AS Maths Bridging the gap Section 1 - Factorising be able to factorise simple expressions be able to factorise quadratics The expression 4x + 8 can be written in factor form,
More informationLesson 7.1: Factoring a GCF
Name Lesson 7.1: Factoring a GCF Date Algebra I Factoring expressions is one of the gateway skills that is necessary for much of what we do in algebra for the rest of the course. The word factor has two
More informationQuadratic Algebra Lesson #2
Quadratic Algebra Lesson # Factorisation Of Quadratic Expressions Many of the previous expansions have resulted in expressions of the form ax + bx + c. Examples: x + 5x+6 4x 9 9x + 6x + 1 These are known
More informationSection 8 2: Multiplying or Dividing Rational Expressions
Section 8 2: Multiplying or Dividing Rational Expressions Multiplying Fractions The basic rule for multiplying fractions is to multiply the numerators together and multiply the denominators together a
More informationDecomposing Rational Expressions Into Partial Fractions
Decomposing Rational Expressions Into Partial Fractions Say we are ked to add x to 4. The first step would be to write the two fractions in equivalent forms with the same denominators. Thus we write: x
More informationMATH 181-Quadratic Equations (7 )
MATH 181-Quadratic Equations (7 ) 7.1 Solving a Quadratic Equation by Factoring I. Factoring Terms with Common Factors (Find the greatest common factor) a. 16 1x 4x = 4( 4 3x x ) 3 b. 14x y 35x y = 3 c.
More informationChapter 5 Self-Assessment
Chapter 5 Self-Assessment. BLM 5 1 Concept BEFORE DURING (What I can do) AFTER (Proof that I can do this) 5.1 I can multiply binomials. I can multiply trinomials. I can explain how multiplication of binomials
More informationALGEBRAIC EXPRESSIONS AND IDENTITIES
9 ALGEBRAIC EXPRESSIONS AND IDENTITIES Exercise 9.1 Q.1. Identify the terms, their coefficients for each of the following expressions. (i) 5xyz 3zy (ii) 1 + x + x (iii) 4x y 4x y z + z (iv) 3 pq + qr rp
More informationACCUPLACER Elementary Algebra Assessment Preparation Guide
ACCUPLACER Elementary Algebra Assessment Preparation Guide Please note that the guide is for reference only and that it does not represent an exact match with the assessment content. The Assessment Centre
More informationTruss Example in Two-Dimensions. Ambar K. Mitra
Truss Example in Two-Dimensions Ambar K. Mitra This document contains screen-shots from the software Statics-Power. Visit www.actuspotentia.com for details. What is a truss? A truss is an assembly of two
More informationFactoring. Difference of Two Perfect Squares (DOTS) Greatest Common Factor (GCF) Factoring Completely Trinomials. Factor Trinomials by Grouping
Unit 6 Name Factoring Day 1 Difference of Two Perfect Squares (DOTS) Day Greatest Common Factor (GCF) Day 3 Factoring Completely Binomials Day 4 QUIZ Day 5 Factor by Grouping Day 6 Factor Trinomials by
More informationEDULABZ INTERNATIONAL NUMBERS AND REAL NUMBERS
5 NUMBERS AND REAL NUMBERS. Find the largest 4-digit number which is exactly divisible by 459. Ans.The largest 4-digit natural number = 9999 We divide 9999 by 459 and find the remainder 459 9999 98 89
More information-5y 4 10y 3 7y 2 y 5: where y = -3-5(-3) 4 10(-3) 3 7(-3) 2 (-3) 5: Simplify -5(81) 10(-27) 7(9) (-3) 5: Evaluate = -200
Polynomials: Objective Evaluate, add, subtract, multiply, and divide polynomials Definition: A Term is numbers or a product of numbers and/or variables. For example, 5x, 2y 2, -8, ab 4 c 2, etc. are all
More informationFactors of 10 = = 2 5 Possible pairs of factors:
Factoring Trinomials Worksheet #1 1. b 2 + 8b + 7 Signs inside the two binomials are identical and positive. Factors of b 2 = b b Factors of 7 = 1 7 b 2 + 8b + 7 = (b + 1)(b + 7) 2. n 2 11n + 10 Signs
More informationAlgebra Module A33. Factoring - 2. Copyright This publication The Northern Alberta Institute of Technology All Rights Reserved.
Algebra Module A33 Factoring - 2 Copyright This publication The Northern Alberta Institute of Technology 2002. All Rights Reserved. LAST REVISED November, 2008 Factoring - 2 Statement of Prerequisite
More informationStudy P.5 CVC 1 7, # 1, 5, 9,...37, 39 55, 59, 65, 69, 73,
GOALS: Factor Polynomials using: 1. Distributive Property (common factors) 2. Trial and Error (trinomials) 3. Factor by Grouping (trinomials) Study P.5 CVC 1 7, # 1, 5, 9,...37, 39 55, 59, 65, 69, 73,...
More informationTERMINOLOGY 4.1. READING ASSIGNMENT 4.2 Sections 5.4, 6.1 through 6.5. Binomial. Factor (verb) GCF. Monomial. Polynomial.
Section 4. Factoring Polynomials TERMINOLOGY 4.1 Prerequisite Terms: Binomial Factor (verb) GCF Monomial Polynomial Trinomial READING ASSIGNMENT 4. Sections 5.4, 6.1 through 6.5 160 READING AND SELF-DISCOVERY
More informationMATD 0370 ELEMENTARY ALGEBRA REVIEW FOR TEST 3 (New Material From: , , and 10.1)
NOTE: In addition to the problems below, please study the handout Exercise Set 10.1 posted at http://www.austin.cc.tx.us/jbickham/handouts. 1. Simplify: 5 7 5. Simplify: ( 6ab 5 c )( a c 5 ). Simplify:
More information7.1 Review for Mastery
7.1 Review for Mastery Factors and Greatest Common Factors A prime number has exactly two factors, itself and 1. The number 1 is not a prime number. To write the prime factorization of a number, factor
More informationChapter 6: Quadratic Functions & Their Algebra
Chapter 6: Quadratic Functions & Their Algebra Topics: 1. Quadratic Function Review. Factoring: With Greatest Common Factor & Difference of Two Squares 3. Factoring: Trinomials 4. Complete Factoring 5.
More informationPolynomial and Rational Expressions. College Algebra
Polynomial and Rational Expressions College Algebra Polynomials A polynomial is an expression that can be written in the form a " x " + + a & x & + a ' x + a ( Each real number a i is called a coefficient.
More informationMATH 141 (Extra Practice 1)
MATH 141 (Extra Practice 1) 1. If matrices A = w 0.5 3 2 values of y and w? and B = 4 1 y 2 are inverses of each other, what are the 2. The company that produces a toothpaste has a fixed costs of $5000.
More information9/16/ (1) Review of Factoring trinomials. (2) Develop the graphic significance of factors/roots. Math 2 Honors - Santowski
(1) Review of Factoring trinomials (2) Develop the graphic significance of factors/roots (3) Solving Eqn (algebra/graphic connection) 1 2 To expand means to write a product of expressions as a sum or difference
More informationPage Points Score Total: 100
Math 1130 Spring 2019 Sample Midterm 3a 4/11/19 Name (Print): Username.#: Lecturer: Rec. Instructor: Rec. Time: This exam contains 9 pages (including this cover page) and 9 problems. Check to see if any
More information7.1 Simplifying Rational Expressions
7.1 Simplifying Rational Expressions LEARNING OBJECTIVES 1. Determine the restrictions to the domain of a rational expression. 2. Simplify rational expressions. 3. Simplify expressions with opposite binomial
More informationDELHI PUBLIC SCHOOL, M R NAGAR, MATHURA, REVISION ASSIGNMENTS, CLASS VIII, MATHEMATICS
CHAPTER: COMPARING QUANTITIES TOPIC: RATIO, PERCENTAGE AND PERCENTAGE INCREASE/DECREASE: SET : 1 1. Rajesh decided to cycle down to his grandma s house. The house was 42 km away from his house. He cycled
More informationUniversity of Phoenix Material
1 University of Phoenix Material Factoring and Radical Expressions The goal of this week is to introduce the algebraic concept of factoring polynomials and simplifying radical expressions. Think of factoring
More informationTool 1. Greatest Common Factor (GCF)
Chapter 7: Factoring Review Tool 1 Greatest Common Factor (GCF) This is a very important tool. You must try to factor out the GCF first in every problem. Some problems do not have a GCF but many do. When
More information25 Increasing and Decreasing Functions
- 25 Increasing and Decreasing Functions It is useful in mathematics to define whether a function is increasing or decreasing. In this section we will use the differential of a function to determine this
More informationS3 (3.1) Mutiplying out brackets & Factorising.notebook February 09, 2016
Daily Practice 30.11.15 Q1. State the equation of the line that passes through (0, 8) and (3, 1) Q2. Simplify 500 Today we will be marking the check-up, homework and revising over multiplying out and simplifying.
More information2.07 Factoring by Grouping/ Difference and Sum of Cubes
2.07 Factoring by Grouping/ Difference and Sum of Cubes Dr. Robert J. Rapalje, Retired Central Florida, USA This lesson introduces the technique of factoring by grouping, as well as factoring the sum and
More information5.1 Exponents and Scientific Notation
5.1 Exponents and Scientific Notation Definition of an exponent a r = Example: Expand and simplify a) 3 4 b) ( 1 / 4 ) 2 c) (0.05) 3 d) (-3) 2 Difference between (-a) r (-a) r = and a r a r = Note: The
More informationMultiply the binomials. Add the middle terms. 2x 2 7x 6. Rewrite the middle term as 2x 2 a sum or difference of terms. 12x 321x 22
Section 5.5 Factoring Trinomials 349 Factoring Trinomials 1. Factoring Trinomials: AC-Method In Section 5.4, we learned how to factor out the greatest common factor from a polynomial and how to factor
More informationGreatest Common Factor and Factoring by Grouping
mil84488_ch06_409-419.qxd 2/8/12 3:11 PM Page 410 410 Chapter 6 Factoring Polynomials Section 6.1 Concepts 1. Identifying the Greatest Common Factor 2. Factoring out the Greatest Common Factor 3. Factoring
More information6-3 Dividing Polynomials
Polynomials can be divided using long division just like you learned with numbers. Divide) 24 6 5 6 24-8 4-0 4 Remainder 24 6 = 5 4 6 Example : Using Long Division to Divide a Polynomial Divide using
More information1/14/15. Objectives. 7-5 Factoring Special Products. Factor perfect-square trinomials. Factor the difference of two squares.
Objectives Factor perfect-square trinomials. Factor the difference A trinomial is a perfect square if: The first and last terms are perfect squares. The middle term is two times one factor from the first
More informationYou are responsible for upholding the University of Maryland Honor Code while taking this exam.
Econ 300 Spring 013 First Midterm Exam version W Answers This exam consists of 5 multiple choice questions. The maximum duration of the exam is 50 minutes. 1. In the spaces provided on the scantron, write
More informationSection R.4 Review of Factoring. Factoring Out the Greatest Common Factor
1 Section R.4 Review of Factoring Objective #1: Factoring Out the Greatest Common Factor The Greatest Common Factor (GCF) is the largest factor that can divide into the terms of an expression evenly with
More informationFactoring is the process of changing a polynomial expression that is essentially a sum into an expression that is essentially a product.
Ch. 8 Polynomial Factoring Sec. 1 Factoring is the process of changing a polynomial expression that is essentially a sum into an expression that is essentially a product. Factoring polynomials is not much
More informationNOTES ON (T, S)-INTUITIONISTIC FUZZY SUBHEMIRINGS OF A HEMIRING
NOTES ON (T, S)-INTUITIONISTIC FUZZY SUBHEMIRINGS OF A HEMIRING K.Umadevi 1, V.Gopalakrishnan 2 1Assistant Professor,Department of Mathematics,Noorul Islam University,Kumaracoil,Tamilnadu,India 2Research
More informationCovariance and Correlation. Def: If X and Y are JDRVs with finite means and variances, then. Example Sampling
Definitions Properties E(X) µ X Transformations Linearity Monotonicity Expectation Chapter 7 xdf X (x). Expectation Independence Recall: µ X minimizes E[(X c) ] w.r.t. c. The Prediction Problem The Problem:
More informationFactoring is the process of changing a polynomial expression that is essentially a sum into an expression that is essentially a product.
Ch. 8 Polynomial Factoring Sec. 1 Factoring is the process of changing a polynomial expression that is essentially a sum into an expression that is essentially a product. Factoring polynomials is not much
More informationBinomial Square Explained
Leone Learning Systems, Inc. Wonder. Create. Grow. Leone Learning Systems, Inc. Phone 847 951 0127 237 Custer Ave Fax 847 733 8812 Evanston, IL 60202 Emal tj@leonelearningsystems.com Binomial Square Explained
More informationAlgebra. Chapter 8: Factoring Polynomials. Name: Teacher: Pd:
Algebra Chapter 8: Factoring Polynomials Name: Teacher: Pd: Table of Contents o Day 1: SWBAT: Factor polynomials by using the GCF. Pgs: 1-6 HW: Pages 7-8 o Day 2: SWBAT: Factor quadratic trinomials of
More informationSection R.5 Review of Factoring. Factoring Out the Greatest Common Factor
1 Section R.5 Review of Factoring Objective #1: Factoring Out the Greatest Common Factor The Greatest Common Factor (GCF) is the largest factor that can divide into the terms of an expression evenly with
More informationPartial Fractions. A rational function is a fraction in which both the numerator and denominator are polynomials. For example, f ( x) = 4, g( x) =
Partial Fractions A rational function is a fraction in which both the numerator and denominator are polynomials. For example, f ( x) = 4, g( x) = 3 x 2 x + 5, and h( x) = x + 26 x 2 are rational functions.
More informationSection 7.4 Additional Factoring Techniques
Section 7.4 Additional Factoring Techniques Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Factor trinomials when a = 1. Multiplying binomials
More informationPolynomial is a general description on any algebraic expression with 1 term or more. To add or subtract polynomials, we combine like terms.
Polynomials Lesson 5.0 Re-Introduction to Polynomials Let s start with some definition. Monomial - an algebraic expression with ONE term. ---------------------------------------------------------------------------------------------
More information(2/3) 3 ((1 7/8) 2 + 1/2) = (2/3) 3 ((8/8 7/8) 2 + 1/2) (Work from inner parentheses outward) = (2/3) 3 ((1/8) 2 + 1/2) = (8/27) (1/64 + 1/2)
Exponents Problem: Show that 5. Solution: Remember, using our rules of exponents, 5 5, 5. Problems to Do: 1. Simplify each to a single fraction or number: (a) ( 1 ) 5 ( ) 5. And, since (b) + 9 + 1 5 /
More informationWorksheet A ALGEBRA PMT
Worksheet A 1 Find the quotient obtained in dividing a (x 3 + 2x 2 x 2) by (x + 1) b (x 3 + 2x 2 9x + 2) by (x 2) c (20 + x + 3x 2 + x 3 ) by (x + 4) d (2x 3 x 2 4x + 3) by (x 1) e (6x 3 19x 2 73x + 90)
More informationClass 11 Maths Chapter 8 Binomial Theorem
1 P a g e Class 11 Maths Chapter 8 Binomial Theorem Binomial Theorem for Positive Integer If n is any positive integer, then This is called binomial theorem. Here, n C 0, n C 1, n C 2,, n n o are called
More informationAlgebra I EOC 10-Day STAAR Review. Hedgehog Learning
Algebra I EOC 10-Day STAAR Review Hedgehog Learning Day 1 Day 2 STAAR Reporting Category Number and Algebraic Methods Readiness Standards 60% - 65% of STAAR A.10(E) - factor, if possible, trinomials with
More informationC Target C-1 Extra Practice j..
C Target C-1 Extra Practice j.....blm 5-5... 1. For each expression i) identify the number of terms ii) identify the expression as a monomial, binomial, or trinomial a) -2x2 i) ii) b) a + b2 + s i) ii)
More informationUNIVERSITY OF KWAZULU-NATAL
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: June 006 Subject, course and code: Mathematics 34 (MATH34P Duration: 3 hours Total Marks: 00 INTERNAL EXAMINERS: Mrs. A. Campbell, Mr. P. Horton, Dr. M. Banda
More informationEXERCISE - BINOMIAL THEOREM
BINOMIAL THOEREM / EXERCISE - BINOMIAL THEOREM LEVEL I SUBJECTIVE QUESTIONS. Expad the followig expressios ad fid the umber of term i the expasio of the expressios. (a) (x + y) 99 (b) ( + a) 9 + ( a) 9
More informationFactor Trinomials of the Form ax^2+bx+c
OpenStax-CNX module: m6018 1 Factor Trinomials of the Form ax^+bx+c Openstax Elementary Algebra This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 4.0 By
More informationMath 10 Lesson 2-3 Factoring trinomials
I. Lesson Objectives: Math 10 Lesson 2-3 Factoring trinomials a) To see the patterns in multiplying binomials that can be used to factor trinomials into binomials. b) To factor trinomials of the form ax
More informationMATH 105 CHAPTER 2 page 1
MATH 105 CHAPTER 2 page 1 RATE OF CHANGE EXAMPLE: A company determines that the cost in dollars to manufacture x cases ofcdʼs Imitations of the Rich and Famous by Kevin Connors is given by C(x) =100 +15x
More informationTest 1 Review. When we use scientific notation, we write these two numbers as:
Test 1 Review Test 1: 15 questions total 13 multiple choice worth 6 points each 2 free response questions (worth 10 or 12 points) Scientific Notation: Scientific Notation is a shorter way of writing very
More informationMust be able to divide quickly (at least up to 12).
Math 30 Prealgebra Sec 1.5: Dividing Whole Number Expressions Division is really. Symbols used to represent the division operation: Define divisor, dividend, and quotient. Ex 1 Divide. What can we conclude?
More informationIs the following a perfect cube? (use prime factorization to show if it is or isn't) 3456
Is the following a perfect cube? (use prime factorization to show if it is or isn't) 3456 Oct 2 1:50 PM 1 Have you used algebra tiles before? X 2 X 2 X X X Oct 3 10:47 AM 2 Factor x 2 + 3x + 2 X 2 X X
More informationrepeated 7 digits or more any place L1
Categorization of Vanity Number Annexure-I LEVEL Pattern Sample Description Plus???? AAAAAA 9427 222222 Ending with 6 repeated digits Plus???? UVWXYZ 9427 123456 Ending with 6 ascending digits 94 1111111
More informationAlg2A Factoring and Equations Review Packet
1 Factoring using GCF: Take the greatest common factor (GCF) for the numerical coefficient. When choosing the GCF for the variables, if all the terms have a common variable, take the one with the lowest
More informationExamples of Strategies
Examples of Strategies Grade Essential Mathematics (40S) S Begin adding from the left When you do additions using paper and pencil, you usually start from the right and work toward the left. To do additions
More informationWe begin, however, with the concept of prime factorization. Example: Determine the prime factorization of 12.
Chapter 3: Factors and Products 3.1 Factors and Multiples of Whole Numbers In this chapter we will look at the topic of factors and products. In previous years, we examined these with only numbers, whereas
More informationPolynomials. You would probably be surprised at the number of advertisments and. THEME: Consumerism CHAPTER
CHAPTER 11 Polynomials THEME: Consumerism You would probably be surprised at the number of advertisments and commercials you see daily. Nearly one-fourth of every television hour is commercial time. Some
More informationCollege Loan Corporation Trust I Quarterly Servicing Report. Distribution Period: 7/26/ /25/2016 Collection Period: 7/1/2016-9/30/2016
Quarterly Servicing Report Distribution Period: 7/26/2016 10/25/2016 Collection Period: 7/1/2016 9/30/2016 I. Deal Parameters Student Loan Portfolio Characteristics 7/1/2016 Activity 9/30/2016 A i Portfolio
More informationCollege Loan Corporation Trust I Quarterly Servicing Report. Distribution Period: 10/26/2017-1/25/2017 Collection Period: 10/1/ /31/2016
Quarterly Servicing Report Distribution Period: 10/26/2017 1/25/2017 Collection Period: 10/1/2016 12/31/2016 I. Deal Parameters Student Loan Portfolio Characteristics 10/1/2016 Activity 12/31/2016 A i
More informationIn this section we revisit two special product forms that we learned in Chapter 5, the first of which was squaring a binomial.
5B. SPECIAL PRODUCTS 11 5b Special Products Special Forms In this section we revisit two special product forms that we learned in Chapter 5, the first of which was squaring a binomial. Squaring a binomial.
More informationxyz Degree is 5. See last term.
THE PERFECT SQUARE - COLLEGE ALGEBRA LECTURES Coprights and Author: Kevin Pinegar Chapter 0 PRE-ALGEBRA TOPICS 0.4 Polnomials and Factoring Polnomials And Monomials A monomial is a number, variable or
More informationChapter 14: Capital Structure in a Perfect Market
Chapter 14: Capital Structure in a Perfect Market-1 Chapter 14: Capital Structure in a Perfect Market I. Overview 1. Capital structure: Note: usually use leverage ratios like debt/assets to measure the
More informationFactoring Quadratic Expressions VOCABULARY
5-5 Factoring Quadratic Expressions TEKS FOCUS Foundational to TEKS (4)(F) Solve quadratic and square root equations. TEKS (1)(C) Select tools, including real objects, manipulatives, paper and pencil,
More informationAdd and Subtract Rational Expressions *
OpenStax-CNX module: m63368 1 Add and Subtract Rational Expressions * OpenStax This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 4.0 By the end of this section,
More informationAlg2A Factoring and Equations Review Packet
1 Multiplying binomials: We have a special way of remembering how to multiply binomials called FOIL: F: first x x = x 2 (x + 7)(x + 5) O: outer x 5 = 5x I: inner 7 x = 7x x 2 + 5x +7x + 35 (then simplify)
More informationVirginia - Mathematics Standards of Learning (2009): 5.5 a, 6.7 Virginia - Mathematics Standards of Learning (2016): 5.5.a, 5.5.b,
1 U n t er r ich t splan Estimate Division with Decimals Two Decimal Places Altersgruppe: 6t h Grade, 5 t h Grade Virginia - Mathematics Standards of Learning (2009): 5.5 a, 6.7 Virginia - Mathematics
More informationChapter 2 Algebra Part 1
Chapter 2 Algebra Part 1 Section 2.1 Expansion (Revision) In Mathematics EXPANSION really means MULTIPLY. For example 3(2x + 4) can be expanded by multiplying them out. Remember: There is an invisible
More informationSection 13-1: The Distributive Property and Common Factors
Section 13-1: The Distributive Property and Common Factors Factor: 4y 18z 4y 18z 6(4y 3z) Identify the largest factor that is common to both terms. 6 Write the epression as a product by dividing each term
More informationECONOMICS QUALIFYING EXAMINATION IN ELEMENTARY MATHEMATICS
ECONOMICS QUALIFYING EXAMINATION IN ELEMENTARY MATHEMATICS Friday 2 October 1998 9 to 12 This exam comprises two sections. Each carries 50% of the total marks for the paper. You should attempt all questions
More informationWEEK 1 REVIEW Lines and Linear Models. A VERTICAL line has NO SLOPE. All other lines have change in y rise y2-
WEEK 1 REVIEW Lines and Linear Models SLOPE A VERTICAL line has NO SLOPE. All other lines have change in y rise y- y1 slope = m = = = change in x run x - x 1 Find the slope of the line passing through
More informationFactoring completely is factoring a product down to a product of prime factors. 24 (2)(12) (2)(2)(6) (2)(2)(2)(3)
Factoring Contents Introduction... 2 Factoring Polynomials... 4 Greatest Common Factor... 4 Factoring by Grouping... 5 Factoring a Trinomial with a Table... 5 Factoring a Trinomial with a Leading Coefficient
More information6.1 Greatest Common Factor and Factor by Grouping *
OpenStax-CNX module: m64248 1 6.1 Greatest Common Factor and Factor by Grouping * Ramon Emilio Fernandez Based on Greatest Common Factor and Factor by Grouping by OpenStax This work is produced by OpenStax-CNX
More informationMath Week in Review #1. Perpendicular Lines - slopes are opposite (or negative) reciprocals of each other
Math 141 Spring 2006 c Heather Ramsey Page 1 Section 1.2 m = y x = y 2 y 1 x 2 x 1 Math 141 - Week in Review #1 Point-Slope Form: y y 1 = m(x x 1 ), where m is slope and (x 1,y 1 ) is any point on the
More informationFirrhill High School. Mathematics Department. Level 5
Firrhill High School Mathematics Department Level 5 Home Exercise 1 - Basic Calculations Int 2 Unit 1 1. Round these numbers to 2 significant figures a) 409000 (b) 837500000 (c) 562 d) 0.00000009 (e)
More informationPART I: NO CALCULATOR (200 points)
Prealgebra Practice Final Math 0 OER (Ch. -) PART I: NO CALCULATOR (00 points) (.). Find all divisors of the following numbers. a) b) 7 c) (.). Find the prime factorization of the following numbers. a)
More information