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ASVAB · Factoring and Polynomials

Factor the expression: x² + 5x + 6.

Correct answer

(x + 2)(x + 3)

  1. A (x + 2)(x + 3)
  2. B (x + 1)(x + 6)
  3. C (x + 5)(x + 1)
  4. D (x − 2)(x − 3)

Why this is the answer

To factor x² + 5x + 6, find two numbers that multiply to the constant (6) and add to the middle coefficient (5). Those numbers are 2 and 3, since 2 × 3 = 6 and 2 + 3 = 5. So the factors are (x + 2)(x + 3). You can verify by expanding: (x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6. ✓ The other options either multiply to the wrong constant or add to the wrong middle term. The product-and-sum method is the standard approach for factoring simple quadratics.
Source: ASVAB MK, Factoring Quadratics

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