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Factoring Trinomials

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Warm Up Multiply: 1. (x + 3)(x – 7) 2. (x – 6)(x + 5) 3. (x + 2)(x + 9) 4. (x – 4)(x – 6)

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Math 2 Today’s Question: How do I factor trinomials with a leading coefficient of one?

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Let’s Multiply (x+2)(x+1) = x 2 + x + 2x + 2 = x 2 + 3x + 2 What if we wanted to “undo” Multiplying? Look at the result that we got above: x 2 + 3x + 2 How can I write this as a product of binomials? ( )( ) xx++21

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Ex 1. Factor the Trinomial Always look for a GCF First!! x 2 + 4x + 3 ( )( ) x+31+x GCF??... NO! What #s multiply to equal 3? 3 and 1 What multiplies to equal x 2 x continued

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Ex.1) Continued (x + 3)(x + 1) How do I know this is right? Look at the product of the outer and inner terms. Do they add to give you the middle term? YES….so you factored it correctly! 3x + x = 4x 3x x

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Ex.2) Factor the Trinomial x 2 + 5x + 6 ( )( ) So, do we use 2 and 3 or 1 and 6? Well…which ones will add to give you 5? 2 and 3!! Check! 3x + 2x = 5x 6 2, 3 1, 6 x2x2 x, x x+23+x 2x 3x GCF??... NO!

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Ex. 3) Factor the Trinomial x 2 – 2x – 3 ( )( ) -3x2x2 -3, 1 -1, 3 x, x x-31+x So, do we use -3 and 1 or -1 and 3? Well…which ones will add to give you -2? -3 and 1!! Check! x + -3x = -2x -3x x GCF??... NO!

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Practice Factor the following: 1. x 2 + 9x x 2 – 12x x 2 – 2x – 3 4. x 2 + 8x + 15

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Factoring with GCF *****Always look for a GCF first***** Ex. 4x 2 – 12x – 16 What is the GCF? 4(x 2 – 3x – 4) Can we factor x 2 – 3x – 4 more? Are there two numbers that multiply to equal -4 and add to be -3? x 2 – 3x – 4 factors to (x – 4)(x + 1) Final answer: 4(x – 4)(x + 1)

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Factoring with GCF Example 2: 6x x + 36 GCF? 6 6(x 2 + 5x + 6) Can be x 2 + 5x + 6 factored? x 2 + 5x + 6 can be factored to (x + 3)(x + 2) Answer: 6(x + 3)(x + 2)

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Practice!! Factor each Polynomial !!! 1.2(x + 2) (x + 6) 2.3x(x + 5) (x – 2) 3.x(x + 7) (x – 2) 4.3(x + 5) (x + 4) 5.4(x – 4) (x + 3) 6.2x(x - 6)(x + 4) Don’t forget the GCF!

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Class work-begin Factoring WS Homework -Finish Factoring WS

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