Math adv function

An unknown polynomial f(x) of degree 37 yields a remainder of 1 when divided by x – 1, a remainder of 3 when divided by x – 3, a remainder of 21 when divided by x – 5.
Find the remainder when f(x) is divided by (x – 1)(x – 3)(x – 5).

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  1. If you divide by a cubic polynomial, the remainder will be a quadratic, r(x) = ax^2+bx+c

    Now, you know that
    r(1) = 1
    r(3) = 3
    r(5) = 21

    a+b+c = 1
    9a+3b+c = 3
    25a+5b+c = 21

    r(x) = 2x^2-7x+6

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