1969 AHSME Problems/Problem 34
Problem
The remainder obtained by dividing by is a polynomial of degree less than . Then may be written as:
Solution
Let the polynomial be the quotient when is divided by , and let the remainder , for some real and . Then we can write: . Since it is hard to deal with (it is of degree 98!), we factor as so we can eliminate by plugging in values of and .
,
,
.
Similarly, .
Solving this system of equations gives and . Thus, . Expanding and combining terms, we see that the answer is .
See also
1969 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 33 |
Followed by Problem 35 | |
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