1953 AMC 12 Problem 36 — Solution | LIVE by Po-Shen Loh

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1953 AMC 12 Problem 36

Attempt Problem 36 of the 1953 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1953 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

36.

Determine $m$ so that $4x^2-6x+m$ is divisible by $x-3.$ The obtained value, $m,$ is an exact divisor of:

$12$

$20$

$36$

$48$

$64$

Answer: C

Concepts:factor theorem divisibility polynomial

Difficulty rating: 1280

Small Hint:

Use the factor theorem at $x=3$

Big Hint:

After finding $m,$ test which listed number is divisible by it

Solution:

Divisibility by $x-3$ requires $4(3)^2-6(3)+m=0,$ so $18+m=0$ and $m=-18.$ Of the listed numbers, only $36$ is an exact multiple of $-18.$

Thus, the correct answer is C.

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Problem 37#37 →

Problem 36 in Other Years

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