Question

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

Answer 1

k = -11

Explanation:

Let
`p(x) = x^3-6x^2+kx+10`

And x+2 is a factor of p(x)

Let x+2 = 0 => x = -2

Putting in p(x)

=> p(-2) =
`(-2)^3-6(-2)^2+k(-2)+10`

By remainder theorem, Remainder will be zero

=> 0 = -8-6(4)-2k+10

=> 0 = -8-24+10-2k

=> 0 = -22-2k

=> -2k = 22

Dividing both sides by -2

=> k = -11