Advanced Math practice question

Answer: A. (x + 3)(x + 4)

The two numbers must multiply to 12 and add to 7: 3 and 4. So x² + 7x + 12 = (x + 3)(x + 4). B encodes picking a factor pair of 12 (2 and 6) without checking that the sum equals the middle coefficient (2 + 6 = 8, giving x² + 8x + 12). C encodes ignoring the signs: (x − 3)(x − 4) = x² − 7x + 12, which has the wrong sign on the middle term. D encodes choosing the factor pair 1 and 12 (product 12, sum 13), again failing the sum condition.

Why the other answers are wrong

B. (x + 2)(x + 6)

2 and 6 do multiply to 12, but they add to 8, not 7 — this pair expands to x² + 8x + 12.

C. (x − 3)(x − 4)

Check the signs: (x − 3)(x − 4) = x² − 7x + 12, and the middle term needs to be +7x.

D. (x + 1)(x + 12)

1 and 12 multiply to 12 but add to 13, so this expands to x² + 13x + 12; you need the pair that also sums to 7.

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