Factoring Trinomials

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

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

Let’s Multiply (x+2)(x+1) = x2 + x + 2x + 2 = x2 + 3x + 2 What if we wanted to “undo” Multiplying? Look at the result that we got above: x2 + 3x + 2 How can I write this as a product of binomials? ( )( ) x + 2 x + 1

Ex 1. Factor the Trinomial Always look for a GCF First!! x2 + 4x + 3 ( )( ) GCF??... NO! x + 3 x + 1 What multiplies to equal x2 What #s multiply to equal 3? x • x 3 and 1 continued

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 3x + x = 4x  x

Ex.2) Factor the Trinomial GCF??... NO! 6 x2 x2 + 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  2, 3 1, 6 x, x x + 2 x + 3 2x 3x

Ex. 3) Factor the Trinomial GCF??... NO! x2 – 2x – 3 ( )( ) -3 x2 x - 3 x + 1 -3, 1 -1, 3 x, x -3x 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 

Practice Factor the following: 1. x2 + 9x + 8 2. x2 – 12x + 10

Factoring with GCF *****Always look for a GCF first***** Ex. 4x2 – 12x – 16 What is the GCF? 4(x2 – 3x – 4) Can we factor x2 – 3x – 4 more? Are there two numbers that multiply to equal -4 and add to be -3? x2 – 3x – 4 factors to (x – 4)(x + 1) Final answer: 4(x – 4)(x + 1)

Factoring with GCF Example 2: 6x2 + 30x + 36 GCF? 6 6(x2 + 5x + 6) Can be x2 + 5x + 6 factored? x2 + 5x + 6 can be factored to (x + 3)(x + 2) Answer: 6(x + 3)(x + 2)

Practice!! 2(x + 2) (x + 6) 3x(x + 5) (x – 2) x(x + 7) (x – 2) Factor each Polynomial !!! Don’t forget the GCF! 2(x + 2) (x + 6) 3x(x + 5) (x – 2) x(x + 7) (x – 2) 3(x + 5) (x + 4) 4(x – 4) (x + 3) 2x(x - 6)(x + 4)

Class work-begin Factoring WS Homework-Finish Factoring WS