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Math Forum » Discussions » Math Topics » alt.math.undergrad.independent

Topic: Japanese University Entrance Examination
Replies: 7   Last Post: Mar 20, 2011 10:39 PM

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James

Posts: 12
Registered: 4/20/09
Japanese University Entrance Examination
Posted: Mar 19, 2011 8:17 PM
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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 65x-68
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





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