Solve Quadratics on the ASVAB AFQT with the Factoring Method

By Rod Powers

If you encounter a quadratic equation on an ASVAB AFQT math subtest, don’t panic: you may be able to solve it by simply putting the equation into the quadratic form and then factoring.

The quadratic form is ax2 + bx + c = 0, where a, b, and c are just numbers. All quadratic equations can be expressed in this form, as in the following examples.

  • 2x2 – 4x = 32: This equation can be expressed in the quadratic form as 2x2 + (–4x) + (–32) = 0. In this case, a = 2, b = –4, and c = –32.
  • x2 = 36: You can express this equation as 1x2 + 0x + (–36) = 0. So a = 1, b = 0, and c = –36.
  • 3x2 + 6x + 4 = –33: Expressed in quadratic form, this equation reads 3x2 + 6x + 37 = 0. So a = 3, b = 6, and c = 37.

Ready to factor? How about trying the following equation?

Solve: x2 + 5x + 6 = 0.

The equation is already expressed in quadratic form here (the expression on the left is equal to zero), saving you a little time.

You can use the factoring method for most quadratic equations where a = 1 and c is a positive number.

The first step in factoring a quadratic equation is to draw two sets of parentheses on your scratch paper, and then place an x at the front of each, leaving some extra space after it. As with the original quadratic, the equation should equal zero: (x )(x ) = 0.

The next step is to find two numbers that equal c when multiplied together and equal b when added together. In the example equation, b = 5 and c = 6, so you need to hunt for two numbers that multiply to 6 and add up to 5. For example,

ASVAB_AFQT_1301

and 2 + 3 = 5. In this case, the two numbers you’re seeking are positive 2 and positive 3.

Finally, put these two numbers into your set of parentheses:

(x + 2)(x + 3) = 0 Any number multiplied by zero equals zero, which means that x + 2 = 0 and/or x + 3 = 0. The solution to this quadratic equation is x = –2 and/or x = –3.