Section 3.3 Homework Questions?

Section

Concepts

3.3 Factoring Trinomials: AC-Method

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1. Factoring Trinomials by the AC-Method

Section 3.3 Factoring Trinomials: AC-Method

1. Factoring Trinomials by the AC-Method

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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.

PROCEDURE AC-Method: Factoring ax2 + bx + c (a 0)

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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.

Example 1 Factoring a Trinomial by the AC Method

Factor the trinomial by the ac-method:23 11 6x x

ExampleSolution:

2 Factoring a Trinomial by the AC Method

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Factor the trinomial by the ac-method:24 14 7x x

ExampleSolution:

3 Factoring a Trinomial by the AC Method

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Factor the trinomial by the ac-method:22 10x x

ExampleSolution:

4

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Factoring a Trinomial by the AC Method

Factor the trinomial by the ac-method:26 17 10x x

ExampleSolution:

5

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Factoring a Trinomial by the AC Method

22 7 6x x Factor the trinomial by the ac-method:

TIP:

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One frequently asked question is whether theorder 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:

Example 6 Factoring Trinomials by the AC-Method

Factor the trinomial by the ac-method:

ExampleSolution:

7 Factoring Trinomials by the AC-Method

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Factor the trinomial by the ac-method:24 24 11x x

Example 8 Factoring a Trinomial by the AC-Method

Factor the trinomial by the ac-method:

Example 9 Factoring a Trinomial by the AC-Method

Factor:

Example 10 Factoring a Trinomial by the AC-Method

Factor the trinomial by the ac-method:

Section 3.3 Factoring Trinomials: AC-Method

You Try

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Factor the trinomial by the ac-method26 5 6x x 23 20 12x x a. b.

Section 3.3 Factoring Trinomials: AC-Method

You Try

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Factor the trinomial by the ac-methoda. b.3 23 23 14x x x 240 24 76y x y xy