Factoring Polynomials: x2 + bx + c
1. Put the polynomial in descending order.
2. Factor out a common factor.
3. Make a list of the pairs of factors for the last term. Now add up the pairs.
x2 + 7x + 12
Factors
1, 12
2, 6
3, 4
Sum
13
8
7
4. Set up parenthesis ( __ + __ ) ( __ + __ ).
5. Fill in the first blank in each parenthesis with the variable being used in the
polynomial. Fill in the second blank in each parenthesis with the set of factor
from the list that adds up to the coefficient of your middle term.
(x + 3) (x + 4)
6. Check your factorization by multiplying to see if you get the original polynomial.
(x + 3) (x + 4) = x2 + 4x + 3x + 12 = x2 + 7x + 12
This is our original polynomial so we are done.
7. State your final Answer: The factorization of x2 + 7x + 12 is (x + 3) (x + 4).
Examples:
x2 – 6x + 5
Factors
1, 5
-1, -5
Sum
6
-6
x2 – 2x – 15
The factorization of
x – 6x + 5 is (x – 1) (x – 5).
2
Factors
1, -15
-1, 15
3, -5
-3, 5
Sum
-14
14
-2
2
The factorization of
x2 – 2x – 15 is (x + 3) (x – 5).
***Sometimes you have to consider the negative factors of a number. Remember negative
number time a negative number is a positive number. ***
{Shortcut for signs: If the first sign in the polynomial is a + then both signs are the same as the
last sign of the polynomial. If the first sign is a negative then the signs are different.}
Tri-County Technical College
May 2006
Created by Tonia Faulling