3.3 Homework Questions?

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 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Slide 2

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 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Slide 3

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. Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. AC-Method: Factoring Slide 4 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Slide 4

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

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

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

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

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

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

Copyright (c) The McGraw-Hill Companies, Inc Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 6 Factoring Trinomials by the AC-Method Factor the trinomial by the ac-method: Slide 11 2 Factoring Trinomials by the AC-Method

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

Copyright (c) The McGraw-Hill Companies, Inc Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 8 Factoring a Trinomial by the AC-Method Factor the trinomial by the ac-method: Slide 13 3 Factoring a Trinomial by the AC-Method

Copyright (c) The McGraw-Hill Companies, Inc Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 9 Factoring a Trinomial by the AC-Method Factor: Slide 14 4 Factoring a Trinomial by the AC-Method

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

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 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Slide 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 1717 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Slide 17