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9.5 Factoring Trinomials

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9.5 – Factoring Trinomials Goals / “I can…” Factor trinomials

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9.5 – Factoring Trinomials Remember how to find the factors of a number. Try 24

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9.5 – Factoring Trinomials Look at the binomials (x + 3) (x + 8) If I multiplied them out. x + 8x + 3x + 8 * 3 = x + 11x + 24 Notice that the middle term is the sum of 8 and 3 and the last term is the product of 8 and 3. 2 2

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9.5 – Factoring Trinomials Using this we can factor a trinomial. It is like doing the opposite of FOIL.

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9.5 – Factoring Trinomials a + 13a + 30 What are the factors of 30? Which factors add up to 13? Once you find the correct combination, write the result as two binomials. ( )( ) 2

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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. We’ll work it out in the next few slides.

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y 2 + 6y + 8 1) Factor y 2 + 6y + 8 Create your MAMA table. MultiplyAdd +8 +6 Product of the first and last coefficients Middle coefficient Here’s your task… What numbers multiply to +8 and add to +6? If you cannot figure it out right away, write the combinations. M A

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y 2 + 6y + 8 1) Factor y 2 + 6y + 8 Place the factors in the table. +1, +8 -1, -8 +2, +4 -2, -4 MultiplyAdd +8 +6 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!

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So your answer would be (x + 2)(x + 4)

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x 2 – 2x – 63 2) Factor x 2 – 2x – 63 Create your MAMA table. MultiplyAdd -63 -2 Product of the first and last coefficients Middle coefficient -63, 1 -1, 63 -21, 3 -3, 21 -9, 7 -7, 9 -62 62 -18 18 -2 2 Signs need to be different since number is negative. M A

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MAMA 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.

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9.5 – Factoring Trinomials TRY: a + 8a + 15 2 MultiplyAdd +15 +8

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

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9.5 – Factoring Trinomials What happens if the middle term is negative? x – 11x + 18 What are the factors of 18 that add up to – 11? 2

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x x Factors of +8: 1 & 8 2 & 4 -1 & -8 -2 & -4 2x + 4x = 6x 1x + 8x = 9x O + I = bx ? -2x - 4x = -6x -1x - 8x = -9x -2 -4

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Check your answer by using FOIL FOIL

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9.5 – Factoring Trinomials TRY: c – 9c + 20 Remember to make your MAMA 2 MultiplyAdd +20 -9

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9.5 – Factoring Trinomials What happens if the last term is negative? p + 8p – 20 Now one term will be positive, one will be negative. BE CAREFUL!!! BE CAREFUL!!! 2

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9.5 – Factoring Trinomials TRY: x – 5x – 24 2

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9.5 – Factoring Trinomials Factors with two variables. This is just like the other problems but both parts will have a variable.

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9.5 – Factoring Trinomials d + 17dg – 60g 22

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