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

Factoring Chart This chart will help you to determine which method of factoring to use. Type Number of Terms 1. GCF 2 or more 2. Diff. Of Squares 2 3. Trinomials 3

Review: (y + 2)(y + 4) y +2 +4 y2 +4y +2y y2 +2y +8 +4y +8 First terms: Outer terms: Inner terms: Last terms: Combine like terms. y2 + 6y + 8 y +2 +4 +4y +2y y2 +2y +8 +4y +8 In this lesson, we will begin with y2 + 6y + 8 as our problem and finish with (y + 2)(y + 4) as our answer.

Here we go! 1) Factor y2 + 6y + 8 Use your factoring chart. Do we have a GCF? Is it a Diff. of Squares problem? Now we will learn Trinomials! You will set up a table with the following information. Nope! No way! 3 terms! Product of the first and last coefficients Middle coefficient 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.

1) Factor y2 + 6y + 8 Create your MAMA table. Multiply Add +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.

1) Factor y2 + 6y + 8 Place the factors in the table. Multiply Add +8 +6 +1, +8 -1, -8 +2, +4 -2, -4 +9, NO -9, NO +6, YES!! -6, NO Which has a sum of +6? We are going to use these numbers in the next step!

Now, group the first two terms and the last two terms. 1) Factor y2 + 6y + 8 Multiply Add +8 +6 +2, +4 +6, YES!! Hang with me now! Replace the middle number of the trinomial with our working numbers from the MAMA table y2 + 6y + 8 y2 + 2y + 4y + 8 Now, group the first two terms and the last two terms.

We have two groups! (y2 + 2y)+(+4y + 8) Almost done! Find the GCF of each group and factor it out. y(y + 2) +4(y + 2) (y + 2)(y + 4) Tadaaa! There’s your answer… (y + 2) (y + 4) You can check it by multiplying. Piece of cake, huh? There is a shortcut for some problems too! (I’m not showing you that yet…) If things are done right, the parentheses should be the same. Factor out the GCF’s. Write them in their own group.

2) Factor x2 – 2x – 63 Create your MAMA table. Multiply Add -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.

Replace the middle term with our working numbers. x2 – 2x – 63 x2 – 9x + 7x – 63 Group the terms. (x2 – 9x) (+ 7x – 63) Factor out the GCF x(x – 9) +7(x – 9) The parentheses are the same! Weeedoggie! (x – 9)(x + 7)

Here are some hints to help you choose your factors in the MAMA 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.

2) Factor 5x2 - 17x + 14 Create your MAMA table. Multiply Add +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. 5x2 – 7x – 10x + 14 Group the terms.

The parentheses are the same! Weeedoggie! (5x – 7)(x – 2) (5x2 – 7x) (– 10x + 14) Factor out the GCF x(5x – 7) -2(5x – 7) The parentheses are the same! Weeedoggie! (5x – 7)(x – 2) Hopefully, these will continue to get easier the more you do them.

Factor x2 + 3x + 2 (x + 2)(x + 1) (x – 2)(x + 1) (x + 2)(x – 1)

Factor 2x2 + 9x + 10 (2x + 10)(x + 1) (2x + 5)(x + 2) (2x + 2)(x + 5)

Factor 6y2 – 13y – 5 (6y2 – 15y)(+2y – 5) (2y – 1)(3y – 5)

Find the GCF! 2(x2 – 7x + 6) Now do the MAMA table! 2) Factor 2x2 - 14x + 12 Find the GCF! 2(x2 – 7x + 6) Now do the MAMA table! Multiply Add +6 -7 Signs need to be the same as the middle sign since the product is positive. -1, -6 -2, -3 -7 -5 Replace the middle term. 2[x2 – x – 6x + 6] Group the terms.

The parentheses are the same! Weeedoggie! 2[(x2 – 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!!