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?