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
[tex]p(x) = x^3 - 4x^2 + cx + 33[/tex]
[tex](-3)^3 - 4(-3)^2 - 3c + 33 = 0[/tex]
[tex]-27 - 36 - 3c + 33 = 0[/tex]
[tex]3c = -30[/tex]
[tex]c = -\frac{30}{3}[/tex]
[tex]c = -10[/tex]
The value of c is -10.
