Difference between revisions of "1950 AHSME Problems/Problem 20"
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== Problem== | == Problem== | ||
− | When <math>x^{13} | + | When <math>x^{13}+1</math> is divided by <math>x-1</math>, the remainder is: |
<math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ -1\qquad\textbf{(C)}\ 0\qquad\textbf{(D)}\ 2\qquad\textbf{(E)}\ \text{None of these answers} </math> | <math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ -1\qquad\textbf{(C)}\ 0\qquad\textbf{(D)}\ 2\qquad\textbf{(E)}\ \text{None of these answers} </math> |
Revision as of 16:50, 11 June 2013
Contents
[hide]Problem
When is divided by , the remainder is:
Solution
Solution 1
Use synthetic division. Notice that no matter what the degree of of the dividend is, the remainder is always
Solution 2
Notice that is a zero of . By the factor theorem, since is a zero, then is a factor of , and when something is divided by a factor, the remainder is
See Also
1950 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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All AHSME Problems and Solutions |