1982 AHSME Problems/Problem 1

Problem

When the polynomial $x^3-2$ is divided by the polynomial $x^2-2$, the remainder is

$\text{(A)} \ 2 \qquad  \text{(B)} \ -2 \qquad  \text{(C)} \ -2x-2 \qquad  \text{(D)} \ 2x+2 \qquad  \text{(E)} \ 2x-2$

Solution

Working out $\frac{x^3-2}{x^2-2}$ using polynomial long division, we get $x + \frac{2x-2}{x^2-2}$. Thus the answer is $2x -2$, for choice $\boxed{(E)}$.

See Also

1982 AHSME (ProblemsAnswer KeyResources)
Preceded by
First Question
Followed by
Problem 2
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