1. 3.3
Homework Questions?

2. 6.3 3.3 Factoring Trinomials: AC-Method Slide 2
Factoring Trinomials: Trial-and-Error Method 1.
Factoring Trinomials by the AC-Method
Slide 2
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Slide 2

3. 6.4 3.3 Factoring Trinomials: AC-Method 1.
Factoring Trinomials by the AC-Method
Factoring Trinomials: AC-Method
To factor a quadratic trinomial,
by the ac-
method, we rewrite the middle term, bx, as a sum or difference of terms. The goal is to produce a four-term polynomial that can be factored by grouping.
Remember the trinomial must be in descending order (in the form ) before beginning the factoring process.
Slide 3
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Slide 3

4. AC-Method: Factoring AC-Method: Factoring ax2 + bx + c (a 0)
Step 1 Factor out the GCF from all terms.
Step 2 Multiply the coefficients of the first and last terms.
Step 3 Find two integers whose product is and whose sum is b. (If no pair of integers can be found, then the trinomial cannot be factored further and is a prime polynomial.)
Step 4 Rewrite the middle term, bx, as the sum of two terms whose coefficients are the integers found in step 3.
Step 5 Factor the polynomial by grouping.
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AC-Method: Factoring
Slide 4
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Slide 4

5. Copyright (c) The McGraw-Hill Companies, Inc
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Factoring a Trinomial by the AC Method
Factor the trinomial by the ac-method:
Slide 5 1
Factoring a Trinomial by the AC Method

6. Factoring a Trinomial by the AC Method2
Factoring a Trinomial by the AC Method
Factor the trinomial by the ac-method:
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Slide 6

7. Factoring a Trinomial by the AC Method3
Factoring a Trinomial by the AC Method
Factor the trinomial by the ac-method:
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Slide 7

8. Factoring a Trinomial by the AC Method4
Factoring a Trinomial by the AC Method
Factor the trinomial by the ac-method:
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Slide 8

9. Factoring a Trinomial by the AC Method5
Factoring a Trinomial by the AC Method
Factor the trinomial by the ac-method:
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Slide 9

10. One frequently asked question is whether the
order matters when we rewrite the middle term of the trinomial as two terms (step 3). The answer is no. From the previous example, the two middle terms in step 3 could have been reversed to obtain the same result:
Slide 10
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Slide 10

11. Copyright (c) The McGraw-Hill Companies, Inc
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Factoring Trinomials by the AC-Method
Factor the trinomial by the ac-method:
Slide 11 2
Factoring Trinomials by the AC-Method

12. Factoring Trinomials by the AC-Method7
Factoring Trinomials by the AC-Method
Factor the trinomial by the ac-method:
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Slide 12

13. Copyright (c) The McGraw-Hill Companies, Inc
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Factoring a Trinomial by the AC-Method
Factor the trinomial by the ac-method:
Slide 13 3
Factoring a Trinomial by the AC-Method

14. Copyright (c) The McGraw-Hill Companies, Inc
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Factoring a Trinomial by the AC-Method
Factor:
Slide 14 4
Factoring a Trinomial by the AC-Method

15. Copyright (c) The McGraw-Hill Companies, Inc
Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 10
Factoring a Trinomial by the AC-Method
Factor the trinomial by the ac-method:
Slide 15 5
Factoring a Trinomial by the AC-Method

16. 6.4 Factoring Trinomials: AC-Method 3.3 You Try 1.
Factor the trinomial by the ac-method
Factoring Trinomials: AC-Method a. b.
Slide 1616
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Slide 16

17. 6.4 Factoring Trinomials: AC-Method 3.3 You Try 1.
Factor the trinomial by the ac-method
Factoring Trinomials: AC-Method a. b.
Slide 1717
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Slide 17