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Objective The student will be able to: factor trinomials with grouping. SOL: A.2c Designed by Skip Tyler, Varina High School.

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Presentation on theme: "Objective The student will be able to: factor trinomials with grouping. SOL: A.2c Designed by Skip Tyler, Varina High School."— Presentation transcript:

1 Objective The student will be able to: factor trinomials with grouping. SOL: A.2c Designed by Skip Tyler, Varina High School

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. Diff. Of Squares 2 3. Trinomials 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? 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. Well work it out in the next few slides.

5 1) Factor y 2 + 6y + 8 Create your MAMA table. MultiplyAdd Product of the first and last coefficients Middle coefficient Heres 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 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 , +4 MultiplyAdd , YES!! Hang with me now! Replace the middle number of the trinomial with our working numbers from the MAMA table 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) Tadaaa! Theres your answer…(y + 4)(y + 2) You can check it by multiplying. Piece of cake, huh? There is a shortcut for some problems too! (Im not showing you that yet…) Factor out the GCFs. Write them in their own group.

9 2) Factor x 2 – 2x – 63 Create your MAMA table. MultiplyAdd Product of the first and last coefficients Middle coefficient -63, 1 -1, , 3 -3, 21 -9, 7 -7, 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) The parentheses are the same! Weeedoggie! (x + 7)(x – 9)

11 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.

12 2) Factor 5x x + 14 Create your MAMA table. MultiplyAdd Product of the first and last coefficients Middle coefficient -1, , , 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

13 (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.

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

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

16 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)

17 2) Factor 2x x + 12 MultiplyAdd Find the GCF! 2(x 2 – 7x + 6) Now do the MAMA table! 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

18 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) Dont forget to follow your factoring chart when doing these problems. Always look for a GCF first!!


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