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

Answer:

The value of c is -10.

Step-by-step 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

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

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

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

$3c = -30$

$c = -\frac{30}{3}$

$c = -10$

The value of c is -10.