How to factor

Step 4 Factoring trinomials

Trinomials: An expression with three terms added together. 2x^² + 6x - 8 will serve as our lucky demonstrator.

First, factor out the GCF. This will ALWAYS be your first step when factoring ANY expression.

2 (x^² + 3x - 4)

If you end up with a power of x greater than two after factoring out the GCF, move on to another step.

List the integer factors of the constant. You'll want two pair them up like so:

-4, 1
-2, 2
-1, 4

You want to find one of these that when added up equals the coefficient of the second term, 3. -1 + 4 = 3. From here, write out two sets of parentheses with x's inside:

(x ) (x )

Then stick the two terms that worked into the parentheses.

(x - 1) (x + 4)

Don't forget to add the GCF back.

2 (x - 1) (x + 4)

That's how you factor a trinomial.

Here's another one: 2x^{^2} + 11x - 6.

There's a twist this time: The coefficient of x^{^2} is not 1. This means that we will be adding another step:

List factors of the constant, -6, as well as the coefficient of x², 2.

-6, 1
-3, 2
-2, 3
-1, 6

1, 2

Now, you'll want to multiply each of the factors on the left side by 1, and on the right by 2. Repeat by switching the 1 and 2. You'll end up with

-6, 2
-3, 4
-2, 6
-1, 12
-12, 1
-6, 2
-4, 3
-2, 6

Find the pair that adds up to the middle term's coefficient, in this case, -1 + 12 = 11. Set up the parentheses:

( x ) ( x )

Stick in the original numbers (that you had before multiplying by 1 and 2):

( x - 1) ( x + 6)

Then stick in the one and two as coefficients of x so that when you multiply the outer and inner terms and add them together, you'll get 11.

(2x - 1) (x + 6)

If you check your work by FOILing it out, you'll end up with 2x^{^2} + 11x - 6, the equation you started with. Congrats!