ASVAB Mathematics Knowledge Practice: Factoring
A lot of algebra involves factoring, so you’re guaranteed to encounter factoring questions on the Mathematics Knowledge subtest on the ASVAB. There are different ways that you can factor an expression, as you’ll see in the following practice questions.
- Factor: 36x2 – 49y2
A. (6x + 7y)(6x – 7y)
C. (6x + 6x)(7y – 7y)
- Factor: x2 – 5x + 6
A. (x – 6)(x + 1)
B. 3(x – 2)(x – 3)
C. x(x – 2) – 3(x – 3)
D. (x – 2)(x – 3)
Answers and explanations
- The correct answer is Choice (A).
When you factor, keep in mind that
That tells you when you have squares, the roots of those squares (which are given in the problem) can be factored out. In this problem,
- The correct answer is Choice (D).
First, write out the two binomials with an x as the first term of each:
Next, insert negative signs in each binominal, because when there’s a positive sign in front of the constant term (here, 6), the signs in the binomials have to match each other. The middle term in the given expression is negative, so the signs in the binomials must both be negative.
Then think of two numbers that multiply to get 6 but add to get 5. The only two numbers that work are 3 and 2:
Last, you can check your work by distributing (or using the FOIL method):
Because you have the original expression, you know you factored correctly.