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.

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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.

Problem 36 in other years