Advanced Math practice question

Answer: -6

Substitute x = 3 into h: h(3) = 3² + k(3) + 9 = 9 + 3k + 9 = 18 + 3k. Setting this equal to 0 gives 3k = −18, so k = −6. (Check: x² − 6x + 9 = (x − 3)², which indeed has the zero x = 3.) The most common errors are (1) answering 6, which comes from solving 3k = 18 after moving 18 to the other side without changing its sign; (2) answering −3, which comes from dividing only the 9 from the constant term (9 + 3k = 0) and ignoring the 3² term; and (3) answering −18, which comes from stopping at 3k = −18 without dividing by 3.

Common wrong answers

If you answered 6

You moved 18 to the other side without changing its sign, solving 3k = 18; it should be 3k = −18, so k = −6.

If you answered -3

You set only 9 + 3k = 0 and ignored the 3² term; h(3) = 9 + 3k + 9 = 18 + 3k.

If you answered -18

You stopped at 3k = −18 — divide by 3 to get k = −6.

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