the remainder theorem - Please Help!!

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i'm really not sure how to do this question.

(3x+2k)^3+(4x-7)^2 has a remainder of 33 when divided by x-3. find k.

i tried to expand the expression, but i don't get a polynomial, so how do i apply the remainder theorem? i would really appreciate it if anyone could tell me how to solve this question! thanks!

  • the remainder theorem - Please Help!! -

    You do not have to expand it,
    the remainder theorem would say here that
    f(3) = 33, so
    (9+2k)^3 + (12-7)^2 = 33
    (9+2k)^3 = 8 , take the cube roo
    9+2k = 2
    2k = -7
    k = -7/2

  • DIVIDE -

    8 DIVIDED BY 200

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