1. I can factor trinomials with grouping.

2. Factoring Chart This chart will help you to determine which method of factoring to use. TypeNumber of Terms 1. GCF 2 or more 2. Grouping 4 3. T-chart 3

3. First terms: Outer terms: Inner terms: Last terms: Combine like terms. y 2 + 6y + 8 y+2 y +4 y2y2 +4y +2y +8 y2y2 +4y +2y +8 Review: (y + 2)(y + 4) In this lesson, we will begin with y 2 + 6y + 8 as our problem and finish with (y + 2)(y + 4) as our answer.

4. Here we go! 1) Factor y 2 + 6y + 8 Use your factoring chart. Do we have a GCF? Do we have four terms? You will set up a table with the following information. Nope! No! 3 terms! Product of the first and last coefficients Sum of the factors The goal is to find two factors in the first column that add up to the middle term in the second column. We’ll work it out in the next few slides.

5. 1) Factor y 2 + 6y + 8 Create your T-Chart MultiplyAdd +8 +6 Product of the first and last coefficients Middle coefficient Here’s your task… What numbers multiply to +8 and add to +6? If you cannot figure it out right away, write the combinations. M A

6. 1) Factor y 2 + 6y + 8 Place the factors in the table. +1, +8 -1, -8 +2, +4 -2, -4 MultiplyAdd +8 +6 Which has a sum of +6? +9, NO -9, NO +6, YES!! -6, NO We are going to use these numbers in the next step!

7. 1) Factor y 2 + 6y + 8 +2, +4 MultiplyAdd +8 +6 +6, YES!! Hang with me now! Replace the middle number of the trinomial with our working numbers from the T-Chart y 2 + 6y + 8 y 2 + 2y + 4y + 8 Now, group the first two terms and the last two terms.

8. We have two groups! (y 2 + 2y) +(4y + 8) If things are done right, the parentheses should be the same. Almost done! Find the GCF of each group and factor it out. y(y + 2) +4(y + 2) (y + 4)(y + 2) You can check it by multiplying. There is a shortcut for these problems when the squared term has a coefficient of 1. Factor out the GCF’s. Write them in their own group.

9. 2) Factor x 2 – 2x – 63 Create your T-Chart MultiplyAdd -63 -2 Product of the first and last coefficients Middle coefficient -63, 1 -1, 63 -21, 3 -3, 21 -9, 7 -7, 9 -62 62 -18 18 -2 2 Signs need to be different since number is negative. M A

10. Replace the middle term with our working numbers. x 2 – 2x – 63 x 2 – 9x + 7x – 63 Group the terms. (x 2 – 9x) (+ 7x – 63) Factor out the GCF x(x – 9) +7(x – 9) (x + 7)(x – 9)

11. Factor x 2 + 3x + 2 1.(x + 2)(x + 1) 2.(x – 2)(x + 1) 3.(x + 2)(x – 1) 4.(x – 2)(x – 1)

12. Try These ( x-5) (x-2) { -25, 2}

13. Here are some hints to help you choose your factors in the T-Chart. 1) When the last term is positive, the factors will have the same sign as the middle term. 2) When the last term is negative, the factors will have different signs.

14. Using the Zero Product Property, you know that either x + 7 = 0 or x - 9 = 0 Solve each equation. x = -7 or x = 9 {-7, 9} To Solve (x + 7)(x - 9) = 0

15. 1)Factor 5x 2 - 17x + 14 Create your T-Chart. MultiplyAdd +70 -17 Product of the first and last coefficients Middle coefficient -1, -70 -2, -35 -7, -10 -71 -37 -17 Signs need to be the same as the middle sign since the product is positive. Replace the middle term. 5x 2 – 7x – 10x + 14 Group the terms. M A

16. (5x 2 – 7x) (– 10x + 14) Factor out the GCF x(5x – 7) -2(5x – 7) The parentheses are the same! Weeedoggie! (x – 2)(5x – 7) Hopefully, these will continue to get easier the more you do them.

17. Factor 2x 2 + 9x + 10 1.(2x + 10)(x + 1) 2.(2x + 5)(x + 2) 3.(2x + 2)(x + 5) 4.(2x + 1)(x + 10)

18. Factor 6y 2 – 13y – 5 1.(6y 2 – 15y)(+2y – 5) 2.(2y – 1)(3y – 5) 3.(2y + 1)(3y – 5) 4.(2y – 5)(3y + 1)

19. 2) Factor 2x 2 - 14x + 12 MultiplyAdd +6 -7 Find the GCF! 2(x 2 – 7x + 6) Now do the T-Chart! -7 -5 Signs need to be the same as the middle sign since the product is positive. Replace the middle term. 2[x 2 – x – 6x + 6] Group the terms. -1, -6 -2, -3

20. 2[(x 2 – x)(– 6x + 6)] Factor out the GCF 2[x(x – 1) -6(x – 1)] The parentheses are the same! 2(x – 6)(x – 1) Don’t forget to follow your factoring chart when doing these problems. Always look for a GCF first!!