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 $\boxed{(E)}$ .

Solution 2

Substituting an easy value, like $3$ , you get $\frac{25}{7}$ , with a remainder of 4. Then you just plug in x to get $E$

-dragoon

1982 AHSME (Problems • Answer Key • Resources)
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1982 AHSME Problems/Problem 1

Contents

Problem

Solution

Solution 2

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