5.3 More on Factoring Trinomials

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 5.3-3

Objective 1 Factor trinomials by grouping when the coefficient of the second-degree term is not 1. Slide 5.3-4

Factor trinomials by grouping when the coefficient of the second-degree term is not 1. 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 5.3-5

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 5.3-6

Factor. Solution: Slide Factoring Trinomials by Grouping CLASSROOM EXAMPLE 1

Factor 6p p 3 + 9p 2. Solution : Slide Factoring a Trinomial with a Common Factor by Grouping CLASSROOM EXAMPLE 2

Objective 2 Factor trinomials by using the FOIL method. Slide 5.3-9

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)

Solution: Factor 6p p Slide Factoring a Trinomial with All Positive Terms by Using FOIL CLASSROOM EXAMPLE 3

Solution: Factor 10m 2 – 23m Slide Factoring a Trinomial with a Negative Middle Term by Using FOIL CLASSROOM EXAMPLE 4

Factor 5p p – 6. Solution: Slide Factoring a Trinomial with a Negative Constant Term by Using FOIL CLASSROOM EXAMPLE 5

Factor 6m mn – 10n 2. Solution: Slide Factoring a Trinomial with Two Variables CLASSROOM EXAMPLE 6

Factor. Solution: Slide Factoring Trinomials with Common Factors CLASSROOM EXAMPLE 7