Name:________________
Date:__________
Factoring Guidelines
Guidelines for Factoring
A. Look for common factors
B. Consider the number of terms
a. Two Terms:
i. Difference of squares
ii. Sum or difference of cubes
b. Three Terms:
i. Trinomial Square
ii. Test Factors of Squares (reverse FOIL)
c. More Than Three Terms:
i. Try Grouping
ii. Try Difference of Squares again
C. Factor Completely
- make sure each factor is a prime factor
Factoring Techniques
A. Common Factors:
Place common factors outside parenthesis
B. Difference of Squares:
A2 – B2 = (A + B)(A – B)
C. Sum or Difference of Cubes:
A3 + B3 = (A + B)(A2 – AB + B2)
A3 – B3 = (A – B)(A2 + AB + B2)
D. Trinomial Squares:
A2 + 2AB + B2 = (A + B)2
A2 – 2AB + B2 = (A – B)2
E. Test Factors:
x2 + bx + c = (x + ___)(x + ___)
* ____ x ____ = c
* ____ + ____ = b
ax2 + bx + c = (___x + ___)(___x + ___)
* use trial an error to fill in blanks
* check with FOIL
F. Grouping:
Insert parenthesis to break up polynomial
Use above methods to factor
Name:________________
Date:__________
Factoring Worksheet
Factor Completely:
1. 8y3 + 4y
2. 3ab – 9ac + 15ad
3. 4x2 + 4x + 1
4. 6x2 – 20x – 16
5. 144xy + 48x2 + 108y2
6. 4a2 – 64b2
7. 4x2 – 9y2
Name:________________
Date:__________
8. y2 + 12y + 36 – 9a2
9. 64a3 + b3
10. 8x3 – 216y3
11. x2 + 7x +12
12. x2 – 12x + 20
13. 2a2 – 18a + 36
14. 16x2 + 32x – 128
15. ax3 – ay3 – bx3 + by3