1955 AMC 12 Problem 25

Attempt Problem 25 of the 1955 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 1955 AMC 12 solutions, or check the answer key.

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25.

One of the factors of

x^4+2x^2+9

is:

x^2+3

x+1

x^2-3

x^2-2x-3

none of these

Rewrite the polynomial as

(x^2+3)^2-(2x)^2

Factor the resulting difference of squares and compare both factors with the choices

We have

\begin{aligned} x^4+2x^2+9 &=(x^2+3)^2\\ &\quad{}-(2x)^2\\ &=(x^2-2x+3)\\ &\quad\cdot(x^2+2x+3). \end{aligned}

Neither factor appears among choices A through D.

Thus, the correct answer is E.

Problem 25 in other years