How to Factor a Three-Term Equation on the ASVAB

By Angie Papple Johnston

If you encounter a question on the ASVAB Math Knowledge test where you have to factor a three-term equation (think: x2 + bx + c), don’t worry: you can use the following steps to get the answer.

  1. Find the factors of the first term of the trinomial.

    The factors of the first term, x2, are x and

    Put those factors (x and x) on the left side of two sets of parentheses: (x)(x).

  2. 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 (–12x) is a negative number, both of the factors must be negative: (x – 0) (x – 0).

  3. 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 –12x. 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 –2x – 10 = 20 (the third term) and –2 + –10 = –12 (the second term). Plug in these numbers: (x – 2) (x – 10).

    Thus, the factors of x2 – 12x + 20 are (x – 2) and (x – 10).