1950 AMC 12 Problem 15

Attempt Problem 15 of the 1950 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 1950 AMC 12 solutions, or check the answer key.

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15.

The real factors of

x^2+4

are:

(x^2+2)(x^2+2)

(x^2+2)(x^2-2)

x^2(x^2+4)

(x^2-2x+2)(x^2+2x+2)

Non-existent

A real linear factor would correspond to a real root

Solving

x^2+4=0

requires

x^2=-4

A real linear factor would give a real root. But

x^2+4=0

implies

x^2=-4,

which has no real solution. Therefore the polynomial has no real linear factors.

Thus, the correct answer is E.

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