Question

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

Answer 1

k=-11

Explanation:

For plato

Answer 2

If a polynomial is divisible by
`x-a`, then
`a` is a root of this polynomial.
Here (x-a) is equal to x+2:


`x-a=x+2 \\ -a=2 \\ a=-2`

So -2 is a root of the polynomial. That means x³-6x²+kx+10=0 for x=-2. Now substitute -2 for x in the equation and solve for k:


`(-2)^3-6 * (-2)^2+ k * (-2)+10=0 \\ -8-6 * 4-2k+10=0 \\ -8-24-2k+10=0 \\ -2k-22=0 \\ -2k=22 \\ \boxed{k=-11}`