Difference between revisions of "1982 AHSME Problems/Problem 1"
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Working out <math>\frac{x^3-2}{x^2-2}</math> using polynomial long division, we get <math>x + \frac{2x-2}{x^2-2}</math>. | Working out <math>\frac{x^3-2}{x^2-2}</math> using polynomial long division, we get <math>x + \frac{2x-2}{x^2-2}</math>. | ||
Thus the answer is <math>2x -2</math>, for choice <math>\boxed{(E)}</math>. | Thus the answer is <math>2x -2</math>, for choice <math>\boxed{(E)}</math>. | ||
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| + | ==Solution 2== | ||
| + | |||
| + | Substituting an easy value, like <math>3</math>, you get <math>\frac{25}{7}</math>, with a remainder of 4. Then you just plug in x to get <math>E</math> | ||
==See Also== | ==See Also== | ||
Revision as of 11:41, 11 September 2022
Contents
Problem
When the polynomial 
is divided by the polynomial 
, the remainder is
Solution
Working out 
using polynomial long division, we get 
.
Thus the answer is 
, for choice 
.
Solution 2
Substituting an easy value, like 
, you get 
, with a remainder of 4. Then you just plug in x to get 
See Also
| 1982 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by First Question |
Followed by Problem 2 | |
| 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 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
