Question

If (x + 2 ) is a factor of x3 − 6x2 + kx + 10, k =

Answer 1

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.

$p(-2)=0 \\ (-2)^3 - 6 \times (-2)^2 + k \times (-2) + 10=0 \\ -8-6 \times 4-2k+10=0 \\ -8-24-2k+10=0 \\ -2k-22=0 \\ -2k=22 \\ k=\frac{22}{-2} \\ \boxed{k=-11}$

Answer 2

Answer:

-11

Step-by-step explanation: