Advanced Math practice question

Answer: A. x + 3 + 1/(x + 2)

(x + 2)(x + 3) = x² + 5x + 6, which is 1 short of x² + 5x + 7. So x² + 5x + 7 = (x + 2)(x + 3) + 1, and dividing by (x + 2) gives x + 3 + 1/(x + 2).

Why the other answers are wrong

B. x + 3

x + 3 is the quotient without its remainder; (x + 2)(x + 3) is x² + 5x + 6, not x² + 5x + 7.

C. x + 3 − 1/(x + 2)

The remainder is +1 (7 − 6), not −1.

D. x + 7 + 1/(x + 2)

x + 7 would come from ignoring the 5x when dividing. Check: (x + 2)(x + 7) = x² + 9x + 14.

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