Section 13.1 The Greatest Common Factor and Factoring by Grouping. to continue. Also, circle your answer to each numbered exercise.

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1 Algebra Foundations First Edition, Elayn Martin-Gay Sec Section 13.1 The Greatest Common Factor and Factoring by Grouping Complete the outline as you view Video Lecture Pause the video as needed to fill in the blanks. Then press Play to continue. Also, circle your answer to each numbered exercise. Objective 1 Find the greatest common factor of a list of integers Finding the GCF (Greatest Common Factor) of a List of Integers Step 1: Write each number as a product of numbers. Step : Identify the prime factors. Step 3: The product of all common prime factors found in Step is the. If there are no common prime factors, the greatest common factor is Find the GCF of 36 and 90. A is a natural number other than 1 whose only factors are 1 and itself. Objective Find the greatest common factor of a list of terms. Find the GCF of x, 3 x and x 5. The GCF of common variable factors is the variable raised to the smallest exponent. 3. Find the GCF of 4 1y and 3 0 y. 34 Copyright 015 Pearson Education, Inc.

2 Algebra Foundations First Edition, Elayn Martin-Gay Sec Section 13.1 The Greatest Common Factor and Factoring by Grouping Objective 3 Factor out the greatest common factor from a polynomial Factor out the GCF x xy+ 7xy 7xy Always check factoring by. FACTORING means. Factor out the GCF. 6. yx ( + ) + 3( x + ) Objective 4 Factor a polynomial by grouping Factor the polynomial. 7. 5xy 15x 6y + 18 Copyright 015 Pearson Education, Inc. 35

3 Algebra Foundations First Edition, Elayn Martin-Gay Sec Section 13.1 The Greatest Common Factor and Factoring by Grouping To Factor by Grouping Step 1: Group the terms in two groups of two terms so that each group has a factor. Step : Factor out the from each group. Step 3: If there is now a common binomial factor in the groups, it out. Step 4: If not, the terms and try these steps again. Factor the polynomial by grouping. 8. 6a + 9ab + 6ab+ 9b 3 36 Copyright 015 Pearson Education, Inc.

4 Algebra Foundations First Edition, Elayn Martin-Gay Sec. 13. Section 13. Factoring Trinomials of the Form x + bx + c Complete the outline as you view Video Lecture 13.. Pause the video as needed to fill in the blanks. Then press Play to continue. Also, circle your answer to each numbered exercise. Objective 1 Factor trinomials of the form x + bx + c Factoring means. Factoring a Trinomial of the Form The product of x + bx+ c is x + bx+ c The product of these numbers is c. x bx c = (x ) (x ) The sum of these numbers is b. Factor the trinomial. 1. x + 7x+ 6 Find two numbers whose product is 6 and whose sum is 7. The order of the factors makes no difference because multiplication is commutative. Factor each trinomial.. x 8x+ 15 Find two numbers whose product is 15 and sum is 8. Copyright 015 Pearson Education, Inc. 37

5 Algebra Foundations First Edition, Elayn Martin-Gay Sec. 13. Section 13. Factoring Trinomials of the Form x + bx + c 3. x 3x x 3xy 4y Objective Factor out the greatest common factor and then factor a trinomial of the form x + bx+ c Factor each trinomial. 5. 3x + 9x xy 5xy 10xy Copyright 015 Pearson Education, Inc.

6 Algebra Foundations First Edition, Elayn Martin-Gay Sec Section 13.3 Factoring Trinomials of the Form ax + bx+ c and Perfect Square Trinomials Complete the outline as you view Video Lecture Pause the video as needed to fill in the blanks. Then press Play to continue. Also, circle your answer to each numbered exercise. Objective 1 Factor trinomials of the form ax + bx+ c, where a 1 Factor x + 31x+ 3. 4x 8x 1 Middle Term = Outside Product + Inside Product Objective Factor out a GCF before factoring a trinomial of the form ax + bx+ c Factor each trinomial x + 38x + 1x Copyright 015 Pearson Education, Inc. 39

7 Algebra Foundations First Edition, Elayn Martin-Gay Sec Section 13.3 Factoring Trinomials of the Form ax + bx+ c and Perfect Square Trinomials 4. x x x x + x x + 14x+ 49 Perfect square trinomial factors as a binomial squared. Factoring Perfect Square Trinomials a + ab+ b = ( a+ b) a ab+ b = ( a b) 40 Copyright 015 Pearson Education, Inc.

8 Algebra Foundations First Edition, Elayn Martin-Gay Sec Section 13.3 Factoring Trinomials of the Form ax + bx+ c and Perfect Square Trinomials Objective 3 Factor perfect square trinomials Factor each perfect square trinomial. 7. x + x x 4xy+ 16y Copyright 015 Pearson Education, Inc. 41

9 Algebra Foundations First Edition, 5th ed., Elayn Martin-Gay Sec Section 13.4 Factoring Trinomials of the Form ax + bx+ c by Grouping Complete the outline as you view Video Lecture Pause the video as needed to fill in the blanks. Then press Play to continue. Also, circle your answer to each numbered exercise. Objective 1 Use the grouping method to factor trinomials of the form ax + bx+ c Factor by grouping. 1. x x x To Factor Trinomials by Grouping Step 1: Factor out a, if there is one other than 1. Step : For the resulting trinomial and whose sum is. ax + bx + c, find two numbers whose product is Step 3: Write the term, bx, using the factors found in Step. Step 4: Factor by. Factor by grouping y 17 y 4 Copyright 015 Pearson Education, Inc.

10 Algebra Foundations First Edition, Elayn Martin-Gay Sec Section 13.4 Factoring Trinomials of the Form ax + bx+ c by Grouping 3. 10x 9x x 7x 7x Copyright 015 Pearson Education, Inc. 43

11 Algebra Foundations First Edition, Elayn Martin-Gay Sec Section 13.5 Factoring Binomials Complete the outline as you view Video Lecture Pause the video as needed to fill in the blanks. Then press Play to continue. Also, circle your answer to each numbered exercise. Objective 1 Factor the difference of squares A contains two terms. Factoring the Difference of Two Squares a b = a+ b a b ( )( ) Factor each binomial. 1. x 4. 11m 100n 3. 16r + 1 The sum of two squares cannot be factored. The sum of two squares is a polynomial. 44 Copyright 015 Pearson Education, Inc.

12 Algebra Foundations First Edition, Elayn Martin-Gay Sec Section 13.5 Factoring Binomials Factor each binomial. 4. xy 9xyz m Objective Factor the sum or difference of two cubes Factoring the Sum or Difference of Two Cubes 3 3 a + b = ( a+ b)( a ab+ b ) 3 3 a b = ( a b)( a + ab+ b ) Factor each sum or difference of two cubes x + 15 Copyright 015 Pearson Education, Inc. 45

13 Algebra Foundations First Edition, Elayn Martin-Gay Sec Section 13.5 Factoring Binomials xy m Copyright 015 Pearson Education, Inc.

14 Algebra Foundations First Edition, Elayn Martin-Gay Sec Section 13.6 Solving Quadratic Equations by Factoring Complete the outline as you view Video Lecture Pause the video as needed to fill in the blanks. Then press Play exercise. to continue. Also, circle your answer to each numbered Objective 1 Solve quadratic equations by factoring Quadratic Equation A quadratic equation is one that can be written in the form ax bx c where a, b and c are real numbers and a = 0 Zero Factor Theorem If a and b are real numbers and if ab = 0, then a = 0 or b = 0. Solve the equation. 1. x + x 8= 0 To use the Zero Factor Theorem, one side of the equation must be a and the other side must be. Copyright 015 Pearson Education, Inc. 47

15 Algebra Foundations First Edition, Elayn Martin-Gay Sec Section 13.6 Solving Quadratic Equations by Factoring Solve the equation.. (x+ 3)(4x 5) = 0 A is a number that makes the equation a true statement. To Solve a Quadratic Equation by Factoring Step 1: Write the equation in so that one side of the equation is 0. Step : the quadratic equation completely. Step 3: Set each factor containing a equal to zero. Step 4: the resulting equations. Step 5: each solution in the original equation. Solve the equation. 3. x(3x 1) = Copyright 015 Pearson Education, Inc.

16 Algebra Foundations First Edition, Elayn Martin-Gay Sec Section 13.6 Solving Quadratic Equations by Factoring Objective Solve equations with degree greater than by factoring Solve the equation. 4. (x+ 3)(x 5x 3) = 0 Objective 3 Find the x-intercepts of the graph of a quadratic equation in two variables Find the x-intercepts of the graph of the equation. 5. y = x + x 11 6 Copyright 015 Pearson Education, Inc. 49

17 Algebra Foundations First Edition, Elayn Martin-Gay Sec Section 13.7 Quadratic Equations and Problem Solving Complete the outline as you view Video Lecture Pause the video as needed to fill in the blanks. Then press Play to continue. Also, circle your answer to each numbered exercise. Objective 1 Solve problems that can be modeled by quadratic equations Remember the steps for solving word problems. Step 1: Step : Step 3: Step 4: 1. The perimeter of a triangle is 85 feet. Find the length of its sides. x+ (x+ 5) + ( x + 3) = 85 x x 5 x 3. An object is thrown upward from the top of an eighty-foot building, with an initial velocity of sixty-four feet per second. The height, h, of the object after t seconds is given by the quadratic equation: h= 16t + 64t+ 80. When will the object hit the ground? 50 Copyright 015 Pearson Education, Inc.

18 Algebra Foundations First Edition, Elayn Martin-Gay Sec Section 13.7 Quadratic Equations and Problem Solving Pythagorean Theorem In a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. leg b leg a hypotenuse c (leg) + (leg) = (hypotenuse) or a + b = c 3. One leg of a right triangle is 4 millimeters longer than the smaller leg and the hypotenuse is 8 millimeters longer than the smaller leg. Find the lengths of the sides of the triangle. x 8 x x 4 Copyright 015 Pearson Education, Inc. 51

19 Algebra Foundations First Edition, Elayn Martin-Gay Sec Section 13.7 Quadratic Equations and Problem Solving 4. The sum of a number and its square is 18. Find the number(s). 5. The product of two consecutive page numbers is 40. Find the page numbers. 5 Copyright 015 Pearson Education, Inc.