Question

If (x+2) is a factor of x^3-6x^2+kx+10, k=

Answer 1

If a binomial $(x-a)$ is a factor of a polynomial, then $a$ is a root of this polynomial.

$(x+2)=(x-(-2)) \Rightarrow a=-2\\\\ (-2)^3-6\cdot(-2)^2+k\cdot(-2)+10=0\\ -8-24-2k+10=0\\ -2k=22\\\ \boxed{k=-11}$