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Section 3.3 Homework Questions?

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Section Concepts 3.3 Factoring Trinomials: AC-Method Slide 2 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Factoring Trinomials by the AC-Method

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Section 3.3 Factoring Trinomials: AC-Method 1.Factoring Trinomials by the AC-Method Slide 3 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 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.

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PROCEDUREAC-Method: Factoring ax 2 + bx + c (a 0) Slide 4 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 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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Example 1Factoring a Trinomial by the AC Method Factor the trinomial by the ac-method:

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Example Solution: 2Factoring a Trinomial by the AC Method Slide 6 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor the trinomial by the ac-method:

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Example Solution: 3Factoring a Trinomial by the AC Method Slide 7 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor the trinomial by the ac-method:

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Example Solution: 4 Slide 8 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factoring a Trinomial by the AC Method Factor the trinomial by the ac-method:

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Example Solution: 5 Slide 9 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factoring a Trinomial by the AC Method Factor the trinomial by the ac-method:

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TIP: Slide 10 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 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:

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Example 6Factoring Trinomials by the AC- Method Factor the trinomial by the ac-method:

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Example Solution: 7Factoring Trinomials by the AC- Method Slide 12 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor the trinomial by the ac-method:

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Example 8Factoring a Trinomial by the AC- Method Factor the trinomial by the ac-method:

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Example 9Factoring a Trinomial by the AC- Method Factor:

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Example 10Factoring a Trinomial by the AC- Method Factor the trinomial by the ac-method:

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Section 3.3 Factoring Trinomials: AC-Method You Try Slide 16 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor the trinomial by the ac-method a. b.

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Section 3.3 Factoring Trinomials: AC-Method You Try Slide 17 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor the trinomial by the ac-method a. b.

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