# ASVAB Preparation: Greatest Common Factor

You will want to brush up on your math skills before going to take the ASVAB. Your task may be to pull out the greatest common factor from two or more terms. Take, for example, this product: 4*xy* + 2*x*^{2}. To factor this product, follow these steps:

- Find the greatest common factor — the highest number that evenly divides all the terms in the expression. Look at both the constants (numbers) and variables. In this case, the highest number that divides into 4 and 2 is 2. And the highest variable that divides into both
*xy*and*x*^{2}is*x*. Take what you know to this point, and you can see that the greatest common factor is 2*x*. - Divide both terms in the expression by the greatest common factor. When you divide 4
*xy*and 2*x*^{2}by 2*x*, the resulting terms are 2*y*+*x*. - Multiply the entire expression (from Step 2) by the greatest common factor (from Step 1) to set the expression equal to its original value. Doing so produces 2
*x*(2*y*+*x*).

Time to try something a little more complicated: factoring a trinomial (an expression with three terms). Suppose you start with *x*^{2} – 12*x* + 20. Follow these steps:

- Find the factors of the first term of the trinomial. The factors of the first term, x
^{2}, are x and x. Put those factors (*x*and*x*) on the left side of two sets of parentheses: (*x*)(*x*). - Determine whether the parentheses will contain positive or negative signs. You can see that the last term in the trinomial (+20) has a plus sign. That means the signs in the parentheses must be either both plus signs or both minus signs. (Why? Because two positive numbers multiplied equals a positive number, and two negative numbers multiplied equals a positive number, but a negative number times a positive number equals a negative number.) Because the second term (–12
*x*) is a negative number, both of the factors must be negative: (*x*– 0)(*x*– 0). - Find the two numbers that go into the right sides of the parentheses. This part can be tricky. The factors of the third term, when added together or subtracted, must equal the second term of the trinomial.

In this example, the third term is 20 and the second term is –12*x*. You need to find the factors of 20 (the third term) that add to give you –12. The two factors you want are –2 and –10, because –2*x* – 10 = 20 (the third term) and –2 + –10 = –12 (the second term). Plug in these numbers: (*x* –2)(*x*–10)

Thus, the factors of *x*^{2} – 12*x* + 20 are (*x* – 2) and (*x* – 10).