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ASVAB · Algebra Basics and Equations

Factor: x² - 9

Reviewed by Jordan Morley, Editorial Lead at 247SimpleTests. Written by the 247SimpleTests Editorial Team from the official source material cited on every question.

Correct answer

(x-3)(x+3)

  1. A (x+3)(x+3)
  2. B (x-3)(x+3)
  3. C (x-3)(x-3)
  4. D (x-9)(x+1)

Why this is the answer

Difference of squares: a² - b² = (a-b)(a+b). Here: x² - 9 = x² - 3² = (x-3)(x+3). Recognise the pattern: a square term minus a perfect-square constant with no middle term is always a difference of squares. The distractors fail when expanded: (x − 3)(x − 3) = x² − 6x + 9 and (x + 3)(x + 3) = x² + 6x + 9 both have a middle term; (x − 9)(x + 1) = x² − 8x − 9. Expanding your chosen factors (FOIL) is the fastest check on the test.
Source: ASVAB MK, Factoring

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About this topic: Algebra Basics and Equations

Algebra basics cover solving linear equations and inequalities, working with expressions, substitution and simple systems. Do the same operation to both sides, and check your answer by substituting it back. This is one of 17 Mathematics Knowledge questions on algebra basics and equations, each with a full explanation on a single study page.

New to this exam? Our ASVAB exam guide explains the format, scoring, and how to prepare.

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