Determine the value(s), if any, of k for which the function f(x) = x^3 + 6x^2 + kx -4 gives the same remainder when divided by x − 1 and x + 2.

Answer 1

first divide I get
x^2 + 7 x +(7+k) with R = 3+k

second divide I get
x^2 + 4 x + (k-8) with R = -2k+12
so
k+3 = -2k+12
3 k = 9
k = 3