Algebra 1B Lesson 21 Instructional Material 1 Factoring trinomials Algebra 1B Lesson 21 Instructional Material 1

REVIEW Steps to factor trinomials: 1.) Look for a GCF 2.) Multiply the first number and the last number 3.) Find the factors of that number (step 2) that add up to the middle term in the trinomial 4.) Replace the middle term with the factors found in step 3 5.) Factor the 4 terms by grouping 6.) Factor each parenthesis (Find the GCF of each parenthesis)

REVIEW Up to this point, we have not had a GCF to factor out in the beginning. We have “skipped” that step, and went on to step 2. Example: x²+9x +18 There’s not a GCF, besides 1 x²+9x +18 (x² + 6x) + (3x + 18) x(x + 6) + 3(x + 6) (x + 6)(x + 3)

Example 1 8x² + 6x – 20 GCF: 2 2(4x² + 3x – 10) Multiply 4 X -10 = -40 Factors of -40 -1 X 40 = 40 -1 + 40 = 39 1 X -40 =-40 1 + -40 = -39 -2 X 20 = -40 -2 + 20 = 18 2 X -20 = -40 2 + -20 = -18 -4 X 10 = -40 -4 +10 = 6

Cont. 8x² + 6x – 20 2(4x² + 3x – 10) 2 (4x² – 5x + 8x – 10)

So, what’s the difference? the gcf that you originally factor out, is carried out through the rest of the problem.

Example 2 3x² – 6x – 9 GCF is 3 3 (x² – 2x – 3) 3 (x² – 3x) + (x – 3)

Example 3…your turn! 6x² – 2x – 20 2 (3x² – x – 10)

Things to remember… Sometimes, you won’t be able to factor a polynomial. If this happens, the trinomial is “PRIME”. Also, once you factor out a GCF, you may not always be able to factor the remaining trinomial. Example: 24x² – 40x + 72 8 ( 3x² – 5x + 9) …Since there aren’t any factors of 27 that add up to a -5, that’s all you can factor this trinomial.