Advanced Math practice question

Answer: A. (x − 1)(x + 5)

This is a difference of squares with (x + 2) as the first square and 3 as the second: (x + 2)² − 3² = (x + 2 − 3)(x + 2 + 3) = (x − 1)(x + 5). Check at x = 3: 25 − 9 = 16 and (2)(8) = 16.

Why the other answers are wrong

B. (x − 1)(x − 5)

The second factor should ADD 3 to (x + 2), giving x + 5. Using −3 in both factors gives (x − 1)², which is (x − 1)(x − 1), not this.

C. (x + 1)(x + 5)

The first factor is (x + 2) − 3 = x − 1, not x + 1. One factor subtracts the 3 and the other adds it.

D. (x + 2)(x − 7)

9 was subtracted from the 2 instead of being square-rooted to 3 and split across the two factors. (x + 2)(x − 7) expands to x² − 5x − 14, far from x² + 4x − 5.

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