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James
Posts:
12
Registered:
4/20/09


Japanese University Entrance Examination
Posted:
Mar 19, 2011 8:17 PM


Hello Mathematicians,
I was looking at a sample question from the aforementioned test, and found this question.
Suppose the polynomial P(x) with integer coefficients satisfies the following conditions. 1. If P(x) is divided by x^2 4x + 3 the remainder is 65x68 2. If P(x) is divided by x^2 + 6x 7, the remainder is 5x + a.
What is a?
I tried letting P(x)/divisor1 = SomeQuotient1 + remainder1/P(x) and P(x)/divisor2 = SomeQuotient2 + remainder2/P(x)
but it doesn't look like this is the right track. Any hints?
Thanks, James



