If a binomial x-a is a factor of a polynomial p(x), then p(a)=0.
x+2 is a factor of p(x)=x³-6x²+kx+10, so p(-2)=0.
\(p(-2)=0 \\
(-2)^3 - 6 \times (-2)^2 + k \times (-2) + 10=0 \\
-8-6 \times 4-2k+10=0 \\
-8-24-2k+10=0 \\
-2k-22=0 \\
-2k=22 \\
k=\frac{22}{-2} \\
\boxed{k=-11}\)
