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Factoring

Factoring. Objective The student will be able to:. Factor trinomials with grouping and Trial & Error. MM1A2f. Review: (y + 2)(y + 4). y 2. First terms: Outer terms: Inner terms: Last terms: Combine like terms. y 2 + 6y + 8. +4y. +2y. y 2. +2y. +8. +4y. +8.

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Factoring

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  1. Factoring

  2. ObjectiveThe student will be able to: Factor trinomials with grouping and Trial & Error. MM1A2f

  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 + 8 Now we will learn Trinomials! You will set up a table with the following information. Product of the first and last coefficients Middlecoefficient 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 Multiply Add+8 +6 1) Factor y2+6y + 8Create your MAMA table. 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. Multiply Add+8 +6 +6, YES!! 1) Factor y2 + 6y + 8 Hang with me now! Create two new binomials with your variable and the values you found in your MAMA table: ( )( ) +2, +4 y + 2 y + 4

  8. y2 + 8 1) Factor. y2 + 6y + 8Put the first and last terms into the box as shown. What are the factors of y2? y and y

  9. y y y2 + 8 1) Factor. y2 + 6y + 8Place the factors outside the box as shown. What are the factors of + 8? +1 and +8, -1 and -8 +2 and +4, -2 and -4

  10. y y y y2 y y2 + 8 + 8 1) Factor. y2 + 6y + 8Which box has a sum of + 6y? + 1 + 2 The second box works. Write the numbers on the outside of box for your solution. y + y + 2y + 8y + 4y + 8 + 4 y

  11. 1) Factor. y2 + 6y + 8 (y + 2)(y + 4) Here are some hints to help you choose your factors. 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. M A Product of the first and last coefficients Middlecoefficient Multiply Add-63 -2 2) Factor x2 – 2x – 63Create your MAMA table. -62 62 -18 18 -2 2 Signs need to be different since number is negative. -63, 1 -1, 63 -21, 3 -3, 21 -9, 7 -7, 9

  13. Multiply Add-63-2 -2, YES!! 1) Factor x2 – 2x – 63 Hang with me now! Create two new binomials with your variable and the values you found in your MAMA table: 7, - 9

  14. x2 - 63 2) Factor. x2 - 2x - 63Put the first and last terms into the box as shown. What are the factors of x2? x and x

  15. x x x2 - 63 2) Factor. x2 - 2x - 63 Place the factors outside the box as shown. What are the factors of - 63? Remember the signs will be different!

  16. x - 7 x x2 -7x + 9 +9x - 63 2) Factor. x2 - 2x - 63Use trial and error to find the correct combination! x - 3 Do any of these combinations work? The second one has the wrong sign! x x2 -3x + 21 +21x - 63

  17. x x x2 - 63 2) Factor. x2 - 2x - 63Change the signs of the factors! + 7 Write your solution. (x + 7)(x - 9) +7x - 9 -9x

  18. 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.

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

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