How to Factor Polynomials
Tutorial Support Services - Mission del Paso Campus
Step 1:
Are there any common factors? If so, factor them out.
Step 2:
How many terms are in the polynomial?
A.
If there are Two terms, decide if one of the following can be applied
1.
Difference of two Squares: (a2 - b2 ) = (a + b)(a - b)
2.
Difference of two Cubes: (a3 - b3) = (a - b)(a2 +ab + b2)
3.
Sum of two cubes:
(a3 + b3) = ( a + b)( a2 - ab + b2)
B.
If there are Three terms, try one of the following.
1.
Perfect Square Trinomial a2 + 2ab + b2 = (a + b)2
2.
Perfect Square Trinomial a2 - 2ab + b2 = (a - b)2
3.
If not a perfect square trinomial, then try factoring by using the AC Method or
Fraction Method.
C.
If there are Four terms, try factoring by grouping.
AC Method of Factoring
2
For Polynomials in the form of: ax + bx + c
3x2 + 11x + 6
2
3x + 9x + 2x + 6
(3x2 + 9x ) (2x + 6)
3x ( x + 3) 2( x + 3)
(3x + 2) (x + 3)
Step 1
Step 2
Step 3
Step 4
Step 5
Step 1
Multiply the first term and the last term of the polynomial, in this example use, 3  6 = 18
Step 2
Now, think of the factors of 18, that when added or subtracted equal 11. It helps to write down all the factors on
scratch paper, then you can clearly, analyze them.
18
Note: In this example the factors you need are 2 and 9 because 2 x 9 = 18 and 2 + 9 = 11
1  18
29
36
Step 3
Now, rewrite the polynomial, but substitute the middle term of the polynomial with the two factors you found. So,
instead of a three-term polynomial, you now have a four-term polynomial. So, now you can factor by grouping.
Step 4
Once you factor by grouping, continue the AC Method by factoring the first group of terms in parenthesis, then
factor the second set of terms in parenthesis.
Step 5
Now, the numbers left on the outside of the parenthesis become one set of factors. And, you should also be able
to factor out a common set of factors, from the two identical sets in parenthesis.
Saved Math Handout (Factoring) AC Method Revised C.Hines 2004
Source: Introductory & Intermediate Algebra for College Students by Robert Blitzer, p.393-403