Question

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!

Answer 1

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

Answer 2

8 DIVIDED BY 200