FACTORING POLYNOMIALS
1) First determine if a common monomial factor (Greatest Common Factor) exists. Factor trees may be used to find the
GCF of difficult numbers. Be aware of opposites: Ex. (a-b) and (b-a) These may become the same by factoring -1
from one of them. 3 12 3 4
3
3
6 6
2) If the problem to be factored is a binomial, see if it fits one of the following situations.
A. Difference of two squares:
9
25
3 53 5
25 5 5 5 5
B. Sum of two squares:
does not factor (it is prime).
C. Sum of two cubes:
8
27
2 34
6 9
Note: Resulting trinomial does not factor.
D. Difference of two cubes:
64 4
4 16
Note: Resulting trinomial does not factor.
E. If none of these occur, the binomial does not factor.
3) If the problem is a trinomial, check for one of the following possibilities.
A. Square of a binomial:
2
6 9 3 3 3
4
20 25
2 5
B. If 1, use reverse foil or trial and error method:
7 12 3 4
7 12 3 4
3 18 6 3
3 18 6 3
C. If 1, use trial and error method. (Grouping may also be used.)
4) If factoring a polynomial with four terms, possible choices are below.
A. Group first two terms together and last two terms together.
5 5 5 5 5 5
3
2 6
3
2 6
3 2 3 3
2
B. Group first three terms together.
6 9
6 9
3
3 3 3 3
C. Group last three terms together.
6 9
6 9
3
3 3 3 3
BE SURE YOUR ANSWERS WILL NOT FACTOR FURTHER!
All answers may be checked by multiplication.
