Advanced Math practice question

Answer: A. (x + 3)² − 7

Half of 6 is 3, and 3² = 9, so x² + 6x = (x + 3)² − 9. Then x² + 6x + 2 = (x + 3)² − 9 + 2 = (x + 3)² − 7. Check by expanding: x² + 6x + 9 − 7 = x² + 6x + 2.

Why the other answers are wrong

B. (x + 3)² + 2

(x + 3)² already contains a +9 that the original expression doesn't have. It must be subtracted back out before the +2 is added: −9 + 2 = −7.

C. (x + 3)² + 11

The 9 was added instead of subtracted. Expanding (x + 3)² + 11 gives x² + 6x + 20, far from the original +2.

D. (x + 6)² − 34

You used the whole 6 instead of half of it. (x + 6)² expands to x² + 12x + 36 — the wrong middle term, which no constant can fix.

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