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

Revision as of 23:29, 9 August 2020

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

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

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 $\boxed{\textbf{(E)}}$ .

1955 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 24	Followed by Problem 26
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50
All AHSME Problems and Solutions

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 ==See Also==
-{{AHSME 50p box|year=1955|before=First Question|num-a=2}}
+{{AHSME 50p box|year=1955|num-b=24|num-a=26}}
 {{MAA Notice}}