Difference between revisions of "1950 AHSME Problems/Problem 20"
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<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> | ||
− | ==Solution 1== | + | ==Solution== |
+ | ===Solution 1=== | ||
Use synthetic division. Notice that no matter what the degree of <math>x</math> of the dividend is, the remainder is always <math>\boxed{\mathrm{(C)}\ 0.}</math> | Use synthetic division. Notice that no matter what the degree of <math>x</math> of the dividend is, the remainder is always <math>\boxed{\mathrm{(C)}\ 0.}</math> | ||
− | ==Solution 2== | + | ===Solution 2=== |
Notice that <math>1</math> is a zero of <math>x^{13} - 1</math>. By the factor theorem, since <math>1</math> is a zero, then <math>x-1</math> is a factor of <math>x^{13} - 1</math>, and when something is divided by a factor, the remainder is <math>\textbf{(C)}0</math> | Notice that <math>1</math> is a zero of <math>x^{13} - 1</math>. By the factor theorem, since <math>1</math> is a zero, then <math>x-1</math> is a factor of <math>x^{13} - 1</math>, and when something is divided by a factor, the remainder is <math>\textbf{(C)}0</math> | ||
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{{AHSME box|year=1950|num-b=19|num-a=21}} | {{AHSME box|year=1950|num-b=19|num-a=21}} | ||
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+ | [[Category:Introductory Algebra Problems]] |
Revision as of 13:22, 17 April 2012
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 AHSME (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 | ||
All AHSME Problems and Solutions |