1. Chapter 6
Section 3

2. 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.

3. 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

4. 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

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

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

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

8. 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

9. 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
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10. 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
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11. EXAMPLE 5 Factor 5p2 + 13p – 6. Solution:
Factoring a Trinomial with a Negative Constant Term
Factor 5p2 + 13p – 6.
Solution:
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12. EXAMPLE 6
Factoring a Trinomial with Two Variables
Factor 6m2 + 11mn – 10n2.
Solution:
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13. Factoring Trinomials with Common Factors
EXAMPLE 7
Factoring Trinomials with Common Factors
Factor.
Solution:
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