Chapter 5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1 Factoring

Copyright © 2011 Pearson Education 2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter – Factoring a Monomial from a Polynomial 5.2 – Factoring by Grouping 5.3 – Factoring Trinomials of the Form ax 2 + bx + c, a = – Factoring Trinomials of the Form ax 2 + bx + c, a ≠ – Special Factoring Formulas and a General Review of Factoring 5.6 – Solving Quadratic Equations Using Factoring 5.7 – Applications of Quadratic Equations Chapter Sections

Copyright © 2011 Pearson Education 3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-3 Factoring Trinomials of the Form ax 2 + bx + c, a ≠ 1

Copyright © 2011 Pearson Education 4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-4 Trial and Error Method 1.Factor out the greatest common factor (GCF), if any. 2.Write all pairs of factors of the coefficient of the squared term, a. 3.Write all pairs of factors of the constant term, c. 4.Try combinations of these factors until the correct middle term, bx, is found.

Copyright © 2011 Pearson Education 5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-5 Trial and Error Method Example: Factor 3x x There is no GCF to factor out. Since the first term is 3x 2, one factor must contain 3x and the other an x. (3x + ?)(x + ?) The product of the last term in the factors must be 12. Only the positive factors of 12 will be considered.

Copyright © 2011 Pearson Education 6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-6 Trial and Error Method Since the product of (3x + 2)and (x + 6) yields the correct term, 20x, they are the correct factors. 3x x + 12 = (3x + 2)(x + 6) Factor 3x x + 12.

Copyright © 2011 Pearson Education 7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-7 Factor by Grouping Method 1.Factor out the greatest common factor, if any. 2.Find two numbers whose product is equal to the product of a times c, and whose sum is equal to b. 3.Rewrite the middle term, bx, as the sum or difference of two terms using the numbers found in step 2. 4.Factor by grouping as explained in Section 5.2.

Copyright © 2011 Pearson Education 8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-8 Factor by Grouping Method Example: Factor 3x x There is no factor common to all three terms. a = 3b = 20c = 12 Find two numbers whose product is a · c and whose sum is b. Factors of 36 (1)(36) (2)(18) Sum of Factors Continued.

Copyright © 2011 Pearson Education 9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-9 Factor by Grouping Method Factor 3x x Use these factors to rewrite 20x. 3x x x 2 + 2x + 18x + 12 Factor by grouping. 3x 2 + 2x + 18x + 12 = x (3x + 2) + 6(3x + 2) = (3x + 2) (x + 6) FOIL to check. Example continued:

Copyright © 2011 Pearson Education 10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-10 Factor by Grouping Method Example: Factor 6x x 2 – 36x. Factor out 3x. 6x x 2 – 36x = 3x (2x 2 + 5x – 12) Rewrite the middle term. 3x (2x 2 + 5x – 12) = 3x (2x 2 + 8x - 3x – 12) Factor by grouping. 3x (2x 2 + 8x - 3x – 12) = 3x[2x(x +4) - 3(x +4)] = 3x (x + 4) (2x – 3) FOIL to check.