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 2 X X X X X X X X 2 X X X 2 X X X X Oct 3 10:46 AM 3
Introduction 4
THIS IS REVIEW b) (b + 5)(b + 3) a) (x + 2)(x + 1)? Example 1 5
???? Key Concepts p. 5 6
To factor a trinomial in the form: Steps: (remember to look for the common factor first!!) 1. Find two numbers that multiply to "c" (constant term) and add to "b" (coefficient of middle term) 2. Write out 2 brackets ax 2 + bx + c, when a = 1 3. Place an "x" at the front of each bracket 4. Write the numbers you found in step #1 at the end of the bracket. **there are some special cases that we will look at that have more than one variable or the exponents will be different, but these are the steps for the general case. EX: x 2 + 7x + 12 x = + = Mar 9 5:50 PM 7
a) x 2 2x 8 b) z 2 12z + 35?? Example 2 8
Factor: 24 5d + d 2? Example 3 9
x 2 15x + 50 y 2 3y 54 m 2 + 14mn + 33n 2 t 2 + 9tu + 20u 2 Mar 11 11:21 AM 10
x 2 + 3x 24 x 2 + 6x + 5 Mar 11 1:25 PM 11
Factor 4t 2 16t + 128? end Example 4 12
Mar 2 10:05 AM 13
Homework: page 165 167: # 4, 7, 9 11, 14, 15 End of lesson 14
Factor: x 2 2x 8 z 2 12z + 35 Example 2 Solution p.1 15
m 2 5m 14 Margin Question 2 16
Expand and simplify: (c + 3)( C 7) (5 x)(9 x) CYU Question 1 17
Factor: x 2 8x + 7 a 2 + 7a 18 CYU Question 2 18
Factor: 30 + 7m + m 2 CYU Question 3 19
Margin Question 5 20
Factor: 5h 2 20h + 60 CYU Question 4 21
How is representing the product of two binomials similar to representing the product of two 2 digit numbers? Discuss the Ideas 1 22
For the multiplication sentence x 2 + ax + b = (x + c)(x + d), what relationships exist among a, b, c and d? Discuss the Ideas 3 23
Common Factors and Simple Trinomials Common Factors: ** first kind of factoring we always look for, no matter how many terms are in the expression. A common factor can be a number, a variable or a combination of the two. Simple Trinomials ** polynomial has 3 terms that are in the form ax 2 + bx + c and a is always 1. Mar 11 10:45 AM 24
Factor each of the following expressions if possible: a) 36x 5 y 4 27x 2 y 5 3x 2 y 3 b) x 2 7x 18 Mar 11 10:50 AM 25
c) x 2 3x 18 d) 2x 2 28x + 48 e) x 2 3xy 18y 2 Mar 11 10:52 AM 26
f) 3x 2 6x + 3 g) 4x 2 12x 16 h) x 2 12xy + 45y 2 i) 12x 3 24x 2 36x Mar 11 10:55 AM 27
j) x 4 + 13x 2 + 42 Simplify: (3x 2) 2 4(2x + 1)(3x 1) (x+ 3)(4x 1) Mar 11 10:58 AM 28
Use prime factorization to find: 1. The GCF of 24 and 36. 2. the LCM of 24 and 36 Mar 11 11:00 AM 29
Mar 12 1:39 PM 30
Review factoring Short Trinomials and GCF Factor this short trinomial: x 2 14x 32 Factor by removing a GCF: 12x 2 y 3 36xy 2 + 48x 3 y 3 z Factor by removing a GCF, then as a short trinomial: 3x 2 24x + 36 Feb 25 9:26 AM 31
Multiply and Factor Difference of Squares Determine each product. THIS IS REVIEW a) (x 5)(x + 5) b) (2x 3)(2x + 3) c) (5x + 7)(5x 7) Do you see a pattern? How could you "do it backwards?" Feb 25 9:19 AM 32
Difference of Squares A difference of squares has the form a 2 b 2. In factored form: a 2 b 2 = (a b) (a + b) Key Concepts p. 4 33
To factor a difference of squares: x 2 y 2 ( )( ) (x )(x ) (x y)(x y) (x + y)(x y) 1. write out 2 brackets. 2. write the square root of first term at the beginning of each bracket 3. write the square root of the last term at the end of each bracket 4. one bracket get a "+" sign, the other a " " sign Mar 26 1:44 PM 34
Multiply and Factor Difference of Squares So can you factor a difference of squares? a) x 2 100 b) 4x 2 49 Feb 25 9:20 AM 35
Factor each binomial: a) 25 36x 2 b) 5x 4 80y 4?? Example 3 36
c) 25y 2 36z 2 d) 49 + 64b 2 Mar 10 9:16 AM 37
Factor: 4x 2 100 x 4 1 Oct 4 1:03 PM 38
pg. 194 4eg, 10, 13ac Mar 25 2:28 PM 39
Multiply and Factor Perfect Square Trinomials THIS IS REVIEW 1. (x + 2) 2 2. (4x + 1) 2 3. (2x 1) 2 Think About It p. 2 40
Mar 27 2:09 PM 41
Mar 27 2:15 PM 42
Multiply and Factor Perfect Square Trinomials Its area is (a + b) 2 = (a + b)(a + b) = a 2 + ab + ab + b 2 = a 2 + 2ab + b 2 Key Concepts p. 1 43
???? Key Concepts p. 2 44
Multiply and Factor Perfect Square Trinomials So can you factor a perfect square trinomial? a) x 2 + 10x + 25 b) x 2 18x + 81 c) 4x 2 20x + 25 Feb 25 9:15 AM 45
?? Example 1 46
Polynomials with Two variables Example: 25x 2 30xy + 9y 2 Oct 3 11:22 AM 47
x 2 + 13x + 36 Sometimes, it won't be possible to factor a perfect square trinomial, and you may have to try another method. Oct 3 11:01 AM 48
Homework page 194 195: # 4(a,b), 7 a, 8(a,c,e) 11(a,c,e), 13(ab) End of lesson 49