Problem:
Suppose and are real numbers. When the polynomial is divided by , the remainder is . When the polynomial is divided by , the remainder is . What is
Answer Choices:
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B.
C.
D.
E.
Solution:
When the polynomial is divided by , the remainder is .
In other words,
When , we obtain
Similarly, When the polynomial is divided by , the remainder is .
In other words,
When , we obtain
However, we know from above that , which gives us and .
Thus,
The problems on this page are the property of the MAA's American Mathematics Competitions