Chapter 6 Section 3
Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. More on Factoring Trinomials Factor trinomials by grouping when the coefficient of the second- degree term is not 1. Factor trinomials by using the FOIL method
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Trinomials such as 2x 2 + 7x + 6, in which the coefficient of the squared term is not 1, are factored with extensions of the methods from the previous sections. More on Factoring Trinomials Slide 6.3-3
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 1 Factor trinomials by grouping when the coefficient of the second-degree term is not 1. Slide 6.3-4
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Recall that a trinomial such as m 2 + 3m + 2 is factored by finding two numbers whose product is 2 and whose sum is 3. To factor 2x 2 + 7x + 6, we look for two integers whose product is 2 · 6 = 12 and whose sum is 7. Sum Product is 2 · 6 = 12 Slide Factor trinomials by grouping when the coefficient of the second-degree term is not 1.
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Factor trinomials by grouping when the coefficient of the second-degree term is not 1. (cont’d) By considering pairs of positive integers whose product is 12, we find the necessary integers to be 3 and 4. We use these integers to write the middle term, 7x, as 7x = 3x + 4x. The trinomial 2x 2 + 7x + 6 becomes Slide 6.3-6
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Factor. Solution: Slide EXAMPLE 1 Factoring Trinomials by Grouping
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Factor 6p p 3 + 9p 2. Solution : Slide EXAMPLE 2 Factoring a Trinomial with a Common Factor by Grouping
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 2 Factor trinomials by using the FOIL method. Slide 6.3-9
Copyright © 2012, 2008, 2004 Pearson Education, Inc. There is an alternative method of factoring that uses trial and error. To factor 2x 2 + 7x + 6 by trial and error, we use the FOIL method in reverse, trying to find two binomials whose products work. If the terms of the original polynomial have greatest common factor 1, then all of that polynomials binomial factors also have GCF 1. Incorrect Correct Slide Factor trinomials by using the FOIL method. (cont’d)
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Factor 6p p Incorrect Correct Slide EXAMPLE 3 Factoring a Trinomial with All Positive Terms by Using FOIL
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Factor 10m 2 – 23m Incorrect Correct Slide EXAMPLE 4 Factoring a Trinomial with a Negative Middle Term by Using FOIL
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Factor 5p p – 6. Solution: Correct Incorrect Slide EXAMPLE 5 Factoring a Trinomial with a Negative Constant Term by Using FOIL
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Factor 6m mn – 10n 2. Solution: CorrectIncorrect Slide EXAMPLE 6 Factoring a Trinomial with Two Variables
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Factor. Solution: Slide EXAMPLE 7 Factoring Trinomials with Common Factors