Factoring Quadratic Trinomials Part 2 (when a is greater than 1)

Steps to Factor if a is not 1: Factor out a GCF if possible 2. Make a double t-chart -On the Left: list factors of “a” -On the Right: list factors of “c” -In the Center: “outsides + insides” Multiply the two outside most factors multiply the two inside most factors, they should add to b 3. Write answer in factored form GCF(#x ± # )(#x ± # ) factors of a become the coefficients, factors of c become the constants the GCF stays on the outside a b c List factors of a Outsides + insides = b List factors of c

Factored Form ( ) ( ) 3x - 4 x + 1 Factor: 3x2 - x - 4 3 -1 -4 3 1 Check for GCF Set up double t-chart none a b c 3 -1 -4 Factors of 3 Outsides + Insides Factors of -4 3 1 3·-4+1·1=-11 1 -4 3 1 3·1 + 1·-4=-1 -4 1 Factored Form ( ) ( ) 3x - 4 x + 1

Factored Form ( ) ( ) x 3x - 3 + 2 Factor: 3x2- 7x - 6 3 -7 -6 3 1 Check for GCF Set up double t-chart none a b c 3 -7 -6 Factors of 3 Outsides + Insides Factors of -6 3 1 3·-6 + 1·1=-17 1 -6 3 1 3·1 + 1·-6=-3 -6 1 3 1 3·3 + 1·-2=7 -2 3 3 1 3·-3 + 1·2=-7 2 -3 Factored Form ( ) ( ) 3x + 2 x - 3

2x( ) ( ) 2x - 1 3x + 5 Factor: 12x3 + 14x2 – 10x 6 7 -5 6 1 1 -5 6 1 Check for GCF Set up double t-chart 2x Use 2x(6x2 + 7x – 5) a b c 6 7 -5 Factors of 6 Outsides + Insides Factors of -5 6 1 6·-5 + 1·1=-29 1 -5 6 1 6·1 + 1·-5=1 -5 1 2 3 2·-5 + 3·1=-7 1 -5 2 3 2·5 + 3·-1=7 -1 5 2x( ) ( ) 2x - 1 3x + 5

Factored Form ( ) ( ) x + 1 2x + 3 Factor: 2x2 + 5x + 3 2 5 3 1 2 Check for GCF Set up double t-chart none a b c 2 5 3 Factors of 2 Outsides + Insides Factors of 3 1 2 1·1+2·3=7 3 1 There aren’t other factors to use, but try a new order – the set up matters! 1 2 1·3+2·1=5 1 3 Factored Form ( ) ( ) x + 1 2x + 3