Difference between revisions of "1955 AHSME Problems/Problem 25"

(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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So the answer must be <math>\boxed{\textbf{(E)}}</math>.
 
So the answer must be <math>\boxed{\textbf{(E)}}</math>.
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==See Also==
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{{AHSME 50p box|year=1955|before=First Question|num-a=2}}
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Revision as of 23:29, 9 August 2020

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
First Question
Followed by
Problem 2
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All AHSME Problems and Solutions


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