Difference between revisions of "1980 AHSME Problems/Problem 28"
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− | Therefore, the left term from <math>x^2n is x^(2n-3u)</math> | + | Therefore, the left term from <math>x^2n</math> is <math>x^{(2n-3u)}</math> |
− | the left term from <math>x^n is x^(n-3v)</math>, | + | the left term from <math>x^n</math> is <math>x^{(n-3v)}</math>, |
If divisible by h(x), we need 2n-3u=1 and n-3v=2 or | If divisible by h(x), we need 2n-3u=1 and n-3v=2 or |
Latest revision as of 12:58, 19 June 2021
Problem
The polynomial is not divisible by if equals
Solution
Assume
Therefore, the left term from is
the left term from is ,
If divisible by h(x), we need 2n-3u=1 and n-3v=2 or
2n-3u=2 and n-3v=1
The solution will be n=1/2 mod(3). Therefore n=21 is impossible
~~Wei
See also
1980 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 27 |
Followed by Problem 29 | |
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All AHSME Problems and Solutions |
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