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if a polynomial leaves a remainder of 5 when divided by x-3 and a reminder of -7 when divided by x+1, what is the reminder when the polynomial is divided by x^2-2x-3?

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  1. Let's say that p(x) = (x-3)(x+1)q(x) + (ax+b)
    That is, it has some linear remainder when divided by x^2-2x-3
    We know from the Remainder Theorem that
    p(3) = 5
    p(-1) = -7
    That means that
    3a+b = 5
    -a+b = -7
    So, a=3, b=-4
    The desired remainder is 3x-4

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