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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. k 2. 4k. k. 1.) Draw box. 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 k2 4k k 1.) Draw box 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. 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 2x2 -8x 2x 1.) Draw box 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. 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. –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 Ok, last example. I wanted to show you one where you have to factor out a negative for your answer. 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 Pretty easy, right???

  7. Happy Factoring!!!

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