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an unknown polynomial f(x) of degree 32 yields a remainder of 1 when divided by x-1 and a remainder of 3 when divided by x-3, find the remainder when f(x) is divided by (x-1)(x-3).

What is the answer? and i was wondering if the part about the polynomial being degree 32 is really relevant

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  1. the remainder will always have degree less than the divisor. So, it will be of the form r(x)=(ax+b)

    So, you know that
    r(1)=1
    r(3)=3

    Now solve for a and b.

    As you surmised, the degree of p(x) does not really matter.

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