Consider the polynomial function f(x)=3x^3-2x^2+kx-3. When f(x) is divided by (x + 2), the remainder is 3. Find the value of k.

Answer 1

If you were to subtract 3 from f(x) then the remainder would be 0 so (x+2) would be a factor and (-2) would be a solution. So solve for f(-2)

3(-2)^3 -2(-2)^2 -2k -3 -3=0

-24 -8 -2k -6=0

-38 -2k=0 2k=-38 k=-19

Answer is k=-19