1. Objective The student will be able to: factor trinomials with grouping. SOL: A.12 Designed by Skip Tyler, Varina High School

2. AIM: How do we factor trinomials of the type x 2 + bx + c? Do Now:Do Now: List all of the factors of the following numbers: 1.24 2.12 3.54 4.56

3. HW Review: Regents Review 10 is due tomorrow.

4. Big Ideas: In earlier courses, you learned how to find the factors of whole numbers like 15. Since 3 x 5 = 15; 3 and 5 are factors of 15. You can also find the factors of some trinomials using similar methods

5. First terms: Outer terms: Inner terms: Last terms: Combine like terms. y 2 + 6y + 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.

6. 1) Factor y 2 + 6y + 8 Create your MA table. 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

7. 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!

8. 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 MAMA table +2 and +4 (y + 2)(y + 4)

9. Now, let’s check our work by FOILing! (y + 2)(y + 4)

10. 2) Factor x 2 – 2x – 63 Create your MA table. 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

11. Replace the factors into two binomials: x 2 – 2x – 63 +7 -9 (x + 7)(x – 9)

12. Here are some hints to help you choose your factors in the MA table. 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.

13. 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)

14. Classwork: During the classwork, please work quickly and quietly in your group. If you have a question, please first ask a groupmate. If no one still knows at that point, please then ask me. The first group to finish will receive HW passes.

15. Summary: What is the most challenging part of factoring trinomials?

16. 2) Factor 5x 2 - 17x + 14 Create your MAMA table. 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

17. (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.

18. 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)

19. 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)

20. 2) Factor 2x 2 - 14x + 12 MultiplyAdd +6 -7 Find the GCF! 2(x 2 – 7x + 6) Now do the MAMA table! -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

21. 2[(x 2 – x)(– 6x + 6)] Factor out the GCF 2[x(x – 1) -6(x – 1)] The parentheses are the same! Weeedoggie! 2(x – 6)(x – 1) Don’t forget to follow your factoring chart when doing these problems. Always look for a GCF first!!