find the value of K such that (x+1) is a factor of x^3-kx^2+x+5

Answer 1

a little synthetic divsion shows that the remainder of the division is 3-k.

We wan the remainder to be zero, so k=3 and we see that

x^3-kx^2+x+5 = (x+1)(x^2-4x+5)