1953 AMC 12 Problem 4

Attempt Problem 4 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).

The roots of

x(x^2+8x+16)(4-x)=0

are:

0

0,

4

0,

4,

-4

0,

4,

-4,

-4

none of these

Factor the quadratic completely

The factor

x^2+8x+16

is a perfect square, so one root is repeated

The equation factors as

x(x+4)^2(4-x)=0.

Its roots, counted with multiplicity, are

0,

4,

-4,

and

-4.

Thus, the correct answer is D.

Problem 4 in other years