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1955 AHSME Problems/Problem 25

Revision as of 22:29, 9 August 2020 by Angrybird029 (talk | contribs) (Created page with "== Problem 25== One of the factors of <math>x^4+2x^2+9</math> is: <math> \textbf{(A)}\ x^2+3\qquad\textbf{(B)}\ x+1\qquad\textbf{(C)}\ x^2-3\qquad\textbf{(D)}\ x^2-2x-3\qqu...")
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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 $\boxed{\textbf{(E)}}$.

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