Factoring Trinomials

A trinomial is a polynomial that has three terms. A polynomial has two or more algebraic terms. The first term has an exponent to the second degree (x2), the second term is x, and the last term is a constant (just any number). Factoring trinomials is an extremely important algebra skill. Factoring polynomials can be tricky however with the detailed explanation below any problem can be solved. 


ax2 + bx + c

a = the x2 term 

b = the x term 

c = the constant value 

Example 1:

a2 + 4a – 12

First identify the values for a, b, and c. 

a = 1

b = 4

c = -12

Remember when no number is in front of a variable, we assume the coefficient is 1. 

Step 2: Find two numbers that when added together produce b and when multiplied together produce c. In this case we should list the factors of -12 first. 

Factors of -12: 

Possible CombinationsDoes c = -12 when multiplied?Does b = 4 when added?Correct Combination
4 x 3127No
4 x -3-121No
-4 x -3 12-7No
-4 x 3-12-1No
6 x 2128No
-6 x 2-12-4No
6 x -2 -124Yes
-6 x -212-8No
12 x 11213No
-12 x 1-12-11No
12 x -1-1211No
-12 x -1 12-13No

The table above shows all the possible combinations for example 1. However only one combination equals both b and c (highlighted in bold). The correct combination of the two numbers should look like this: 

(a – 2) (a + 6) 

We can foil the problem to see if it matches the original problem.

Example 2: 

Factor the following polynomial: 

x2 + 2x -8     

First identify the values of a, b, and c.   

a = 1

b = 2

c =-8   

Now consider the factors of c and when added together equal b. 

Possible CombinationsDoes c = -8 when multiplied?Does b = 2 when added?Correct Combination
8 x 189No
-8 x -18-9No
8 x -1 -87No
-8 x 18-7No
2 x 486No
-2 x 4-82Yes
2 x -4 -8-2No
-2 x -48-8No

The correct combination should look like this:

(x – 2) (x + 4) 

Use the foil method to check it against the original problem. 

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