1. Factoring Review

2. Factoring Chart This chart will help you to determine which method of factoring to use. Type Number of Terms
1. GCF or more
Difference of Squares
Trinomials

3. Always look for a GCF first!
A GCF is something EVERY term has in common
Find the GCF

4. The order does not matter!!
Difference of Squares
a2 - b2 = (a - b)(a + b) or
a2 - b2 = (a + b)(a - b)
The order does not matter!!
Both terms must be perfect squares
Must be subtraction
If x2 doesn’t come first, factor out -1

5. Factor and solve x2 – 25=0 Do you have a GCF? No
Are the Difference of Squares steps true?
Two terms?
1st term a perfect square?
2nd term a perfect square?
Subtraction? No
Yes
Yes
x2 – 25
Yes
Yes
( )( ) x + 5 x - 5
x=5,-5

6. Factor and solve 16x2 – 9=0 Do you have a GCF?
Are the Difference of Squares steps true?
Two terms?
1st term a perfect square?
2nd term a perfect square?
Subtraction? No
16x2 – 9
Yes
Yes
Yes
Yes
(4x )(4x ) + 3 - 3
x= 3/4,-3/4

7. Factor and solve 36x-49x3 Do you have a GCF? Yes! GCF = x x(36-49x2)
Are the Difference of Squares steps true?
Two terms?
1st term a perfect square?
2nd term a perfect square?
Subtraction?
Yes! GCF = x
Yes
-x(49x2 – 36)
Yes
Yes
Yes
-x(7x )(7x ) - + 6 6
x=0,6/7,-6/7

8. Factor and solve 50x + 7x2 x(50+7x) x=0, x=-50/7
You cannot factor using difference of squares because there is no subtraction! But you can still look for GCF
x(50+7x)
x=0, x=-50/7

9. Factoring Trinomials

10. Factoring Trinomials
Step 1: Make sure everything is on one side of the equation
Step 2: Multiply 1st term by last term
Step 3: Set up ( ) for factors and divide by 1st term
Step 4: Find 2 numbers that multiply to last term and add to middle term
Step 5: Simplify fractions, if they do not simplify, bring denominator to the front
Step 6: Set equal to 0 and solve

11. 3x2 – 14x + 8 = 0 x = 4, x = 2/3 1) Multiply 3 • (8) = 24;
2) Set up ( )
( x )( x ) 3 3
What multiplies to 24 and adds to -14?
( x - 12)( x - 2) 3
4) Simplify (if possible).
5) Move denominator(s)in front of “x”.
( x - 4)( 3x - 2)
x = 4, x = 2/3

12. 2x2 – 3x – 9 = 0 x = 3, x = -3/2 1) Multiply 2 • (-9) = -18;
2) Set up ( )
( x )( x ) 2 2
What multiplies to -18 and adds to -3?
( x - 6)( x + 3) 2
4) Simplify (if possible).
5) Move denominator(s)in front of “x”.
( x - 3)( 2x + 3)
x = 3, x = -3/2

13. 6x3 + 13x2 = -6x x = -2/3, x = -3/2 1) Rewrite and factor GCF
2) Multiply 6 • (6) = 36;
x2 + 13x + 36
3) Set up ( )
( x )( x ) 6 6
4) What multiplies to 36 and adds to 13?
( x + 4)( x + 9) 6
5) Simplify (if possible).
5) Move denominator(s)in front of “x”.
(3x + 2)( 2x + 3)
x = -2/3, x = -3/2