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Objective The student will be able to:

Objective The student will be able to:. factor trinomials with grouping. SOL: A.2c. 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

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Objective The student will be able to:

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

  2. Factoring ChartThis 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. Review: (y + 2)(y + 4) y2 First terms: Outer terms: Inner terms: Last terms: Combine like terms. y2 + 6y + 8 +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.

  4. Here we go! 1) Factor y2 + 6y + 8Use your factoring chart. Nope! 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. No way! 3 terms! 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. M A Product of the first and last coefficients Middlecoefficient 8 1) Factor y2+6y + 8Create your X table. 6 Here’s your task… What numbers multiply to +8 and add to +6? If you cannot figure it out right away, write the combinations.

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

  7. Product of the first and last terms Middleterm Multiply Add+8 +6 +6, YES!! 1) Factor y2 + 6y + 8 8y2 +2, +4 2y 4y 6y

  8. y 2 Now we set up our box! y2 + 6y + 8 y2 2y y 4y 8 4 So our factorization is… (y+4)(y+2)

  9. x -9 2) Factor x2 – 2x – 63Create your X-BOX. -63x2 x2 x -9x -9x 7x -63 7 7x -2x So x2 – 2x – 63 = (x + 7)(x – 9)

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

  11. 5x -7 2) Factor 5x2 - 17x + 14Create your X BOX. 70x2 70x2 5x2 5x2 -7x x -10x -7x -10x -63 -2 -17x -17x 5x2 – 17x + 14 = (5x – 7)(x – 2)

  12. Factor x2 + 3x + 2 • (x + 2)(x + 1) • (x – 2)(x + 1) • (x + 2)(x – 1) • (x – 2)(x – 1)

  13. Factor 2x2 + 9x + 10 • (2x + 10)(x + 1) • (2x + 5)(x + 2) • (2x + 2)(x + 5) • (2x + 1)(x + 10)

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

  15. 2) Factor 2x2 - 14x + 12 Find the GCF! 2(x2 – 7x + 6) Now do the X BOX!

  16. Don’t forget to follow your factoring chart when doing these problems. Always look for a GCF first!!

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