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 17:50, 11 June 2013
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 | |
| 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 | ||
