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

2. 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

4. 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

5. 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

6. 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

7. 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