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Factoring Trinomials

Factoring Trinomials. Mrs. Unger’s Method… The Box Method + Part of the Master Product Method. Ex1: k 2 + 9k + 20. +4. k. 1.) Draw box. k 2. 4k. k. 20. +5. 5k. 2.) Write 1 st term in 1 st box, and 3 rd term in 4 th box. 3 .) Find Master Product. (1)(20) = 20. 1, 20

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Factoring Trinomials

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  1. Factoring Trinomials Mrs. Unger’s Method… The Box Method + Part of the Master Product Method

  2. Ex1: k2 + 9k + 20 +4 k 1.) Draw box k2 4k k 20 +5 5k 2.) Write 1st term in 1st box, and 3rd term in 4th box. 3.) Find Master Product (1)(20) = 20 1, 20 2, 10 4, 5 4.) List factors of MP to find two whose sum equals “b”. 5.) Put factors in remaining boxes with variable. **The sign stays with the middle terms.** 6.) Factor out GCF in each row. 7.) Factor out GCF in each column. 8.) Write your answer! (k + 5)(k +4)

  3. Ex2: 2x2 – 11x + 12 -4 x 1.) Draw box 2x2 -8x 2x 12 -3 -3x 2.) Write 1st term in 1st box, and 3rd term in 4th box. 3.) Find Master Product (2)(12) = 24 -1, -24 -2, -12 -3, -8 -4, -6 4.) List factors of MP to find two whose sum equals “b”. 5.) Put factors in remaining boxes with variable. **The sign stays with the middle terms.** 6.) Factor out GCF in each row. 7.) Factor out GCF in each column. 8.) Write your answer! (2x – 3)(x – 4)

  4. Ex3: –10 + 24z – 8z2 Before we can do anything, we have to rearrange. –8z2 + 24z – 10 GCF = –2 And then we have to take out the GCF. **Quadratic term MUST be positive.** –2(4z2 – 12z + 5) (4)(5) = 20 -1, -20 -2, -10 -4, -5 -1 2z 4z2 -2z 2z (2z – 5)(2z – 1) –2 5 -5 -10z But don’t forget that -2 we took out earlier!

  5. Ex4: 15x2 + 13xy + 2y2 But what happens when we have TWO variables??? It’s no big deal. It’s the same method. GCF = 1Well that doesn’t help! Check for the GCF, first. Ok, here we go… (15)(2) = 30 1, 30 2, 15 3, 10 5, 6 +y 5x 15x2 3xy 3x (3x + 2y)(5x + y) 2y2 +2y 10xy

  6. Ex5: a2 – 2a – 35 Check for the GCF, first. GCF = 1Well that doesn’t help! (1)(-35) = -35 1, -35 -1, 35 5, -7 -5, 7 +5 a a2 5a a (a – 7)(a + 5) -35 -7 -7a

  7. Ex6: 5 + 7x – 6x2 Before we can do anything, we have to rearrange. –6x2+ 7x + 5 And then we have to take out the GCF. (6)(-5) = -30 We have to take out a –1 to make the quadratic term positive. 1, -30 -1, 30 2, -15 -2, 15 3, -10 -3, 10 5, -6 -5, 6 –1(6x2 – 7x – 5) – 5 3x 6x2 – 10x 2x –1(3x – 5)(2x + 1) –5 +1 3x Pretty easy, right???

  8. Happy Factoring!!!

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