# 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.

Trinomial

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:

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.

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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