1955 AHSME Problems/Problem 25

Problem 25

One of the factors of $x^4+2x^2+9$ is:

$\textbf{(A)}\ x^2+3\qquad\textbf{(B)}\ x+1\qquad\textbf{(C)}\ x^2-3\qquad\textbf{(D)}\ x^2-2x-3\qquad\textbf{(E)}\ \text{none of these}$

Solution

We can test each of the answer choices by using polynomial division.

$x^2 + 3$ leaves behind a remainder, and so does $x^2 - 3$.

In addition, $x + 1$ also fails the test, and that takes down $x^2 - 2x - 3$, which can be expressed as $(x + 1)(x - 3)$.

So the answer must be $\boxed{\textbf{(E)}}$.

See Also

1955 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 24
Followed by
Problem 26
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