Question

Find the value of c so that (x+3) is a factor of the polynomial p(x). p(x)=x^3-4x^2+cx+33

Answer 1

The value of c is -10.

Explanation:

Since (x+3) is a factor of the polynomial p(x).

We have that:

x + 3 = 0 -> x = -3

So p(-3) = 0

Then

`p(x) = x^3 - 4x^2 + cx + 33`

`(-3)^3 - 4(-3)^2 - 3c + 33 = 0`

`-27 - 36 - 3c + 33 = 0`

`3c = -30`

`c = -(30)/(3)`

`c = -10`

The value of c is -10.