Day 4 Choosing a Factoring Method Learning Goals

Day 4 Choosing a Factoring Method Learning Goals for Multi-Step Factoring 8. 6. 1 Choose an appropriate method for factoring a polynomial. 8. 6. 2 Combine methods for factoring a polynomial. FACTORING METHODS What the problem looks like. . . What the answer looks like. . . Notice that there is a common factor in all 3 terms Notice that there are 3 terms in the answer and a piece out front Notice that there are 4 terms. Notice that there are 2 binomials Notice that there are 3 terms and the first one is squared. Notice that there are 2 binomials Factoring out the GCF Factoring by Grouping Factoring a Polynomial Tell whether each polynomial is completely factored. If not factor it. A. 3 x 2(6 x – 4) C. 5 x 2(x – 1) B. (x 2 + 1)(x – 5) D. (4 x + 4)(x + 1)

Day 4 Choosing a Factoring Method To factor a polynomial completely, you may need to use more than one factoring method. Use the steps below to factor a polynomial completely. Step 1: Factor out the GCF Step 2: Use the number of terms to decide on a factoring method. Step 3: Factor by the appropriate method. Step 4: Check the all elements of the answer to see if any parts could be factored further. Step 5: Check your answer by multiplying it back out and comparing with the original problem. A. Factor 10 x 2 + 48 x + 32 completely. Check your answer. B. Factor 4 x 3 + 16 x 2 + 16 x completely. Check your answer. LG 8. 6. 1

Day 4 Choosing a Factoring Method If none of the factoring methods work, the polynomial is said to be unfactorable. For a polynomial of the form ax 2 + bx + c, if you multiply a and can’t get any of their factor pairs to add up to b then it is UNFACTORABLE. . Factor each polynomial completely. LG 8. 6. 2 A. 9 x 2 + 3 x – 2 B. 12 b 3 + 48 b 2 + 48 b C. 5 x – 20 x 3 + 7 – 28 x 2 D. 2 p 5 + 10 p 4 – 12 p 3