Chapter 6 Section 3

More on Factoring Trinomials 6.3 More on Factoring Trinomials Factor trinomials by grouping when the coefficient of the second-degree term is not 1.

More on Factoring Trinomials Trinomials such as 2x2 + 7x + 6, in which the coefficient of the squared term is not 1, are factored with extensions of the methods from the previous sections. Slide 6.3-3

Objective 1 Factor trinomials by grouping when the coefficient of the second-degree term is not 1. Recall that a trinomial such as m2 + 3m + 2 is factored by finding two numbers whose product is 2 and whose sum is 3. To factor 2x2 + 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 6.3-5

Factor trinomials by grouping when the coefficient of the second-degree term is not 1. (1st Method) 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 2x2 + 7x + 6 becomes Slide 6.3-6

Factor trinomials by grouping when the coefficient of the second-degree term is not 1. (2nd Method) Prime factors of 12 Look for two factors of 12 Whose sum is 7 Divide by 2

Factoring Trinomials by Grouping EXAMPLE 1 Factoring Trinomials by Grouping Factor. Solution: Slide 6.3-7

EXAMPLE 2 Solution: Factor 6p4 + 21p3 + 9p2. Solution: Factoring a Trinomial with a Common Factor by Grouping Solution: Factor 6p4 + 21p3 + 9p2. Solution: Look for two factors of 6 whose sum is 7 Divide by 2 Slide 6.3-8

EXAMPLE 3 Factor 6p2 + 19p + 10. Solution: Factoring a Trinomial with All Positive Terms Factor 6p2 + 19p + 10. Solution: Look for two factors of 60 whose sum is 19 Divide by 6 Slide 6.3-11

EXAMPLE 4 Factor 10m2 – 23m + 12. Solution: Factoring a Trinomial with a Negative Middle Term Factor 10m2 – 23m + 12. Solution: Look for two factors of 120 whose sum is -23 Slide 6.3-12

EXAMPLE 5 Factor 5p2 + 13p – 6. Solution: Factoring a Trinomial with a Negative Constant Term Factor 5p2 + 13p – 6. Solution: Slide 6.3-13

EXAMPLE 6 Factoring a Trinomial with Two Variables Factor 6m2 + 11mn – 10n2.   Solution: Slide 6.3-14

Factoring Trinomials with Common Factors EXAMPLE 7 Factoring Trinomials with Common Factors Factor. Solution: Slide 6.3-15