How to Factor Binomials

By eHow Contributor

Before you learn to factor higher-order polynomials, you need to learn binomials inside and out. If you understand the basic building blocks of algebra, it will make more advanced lessons easier.


Step 1

Many numbers and polynomial terms can be made by multiplying two or more numbers or terms together. For example, 9 can be factored as 3 * 3, and x^2 + x can be factored as (x)(x + 1). Factoring is basically the process of turning a term into a series of simpler terms multiplied together.

Step 2

Any number or variable that is a factor of both terms in a binomial can be factored out. For example, the binomial 3x^3 + 6x can be factored to (3x)(x^2 + 2) because 3x is a factor of 3x^2 (which is 3x * x^2) and of 6 (which is 3x * 2).

Step 3

Find the greatest common factor (GCF) of both terms. The greatest common factor is the largest value that can be factored out of both terms. In the expression 6y^2 - 24, 3 is a common factor of both terms, but it is not the GCF. Six is the GCF, since both numbers can be divided by 6. Factoring it out, we get 6(y^2 - 4).

Step 4

Find out if you have a difference of squares. A difference of squares is a variable squared minus a constant, like y^2 - 4. If you have factored out the GCF and don't have a minus sign in your binomial, you are done.

Step 5

Solve the difference of squares. First make sure the numbers are arranged in the proper order, with the positive term before the negative term, then find the square root of each term. In the example above, the square root of y^2 is y, and the square root of 4 is 2.

Step 6

Set up two sets of parentheses. Each will have the first square root followed by the second square root. In the first, they will be separated by a addition sign, and in the second, a subtraction sign. To take the example from steps 3 and 4, we get y^2 - 4 = (y + 2)(y - 2). Looking at the whole problem for step 3, we get 6y^2 - 24 = 6(y^2 - 4) = 6(y + 2)(y - 2).