Question

Use the Factor Theorem to determine whether the binomial x-3 is a factor of the polynomial function f(x)=-5x^3+16x^2-9.

A. No, because f(c) = -18
B. Yes
C. No, because f(c) = -288
D. No, because f(c) = 270

Answer 1

After calculating f(3) and finding it equals zero, we can confirm that the binomial x-3 is a factor of the polynomial f(x), according to the Factor Theorem.

Step-by-step explanation:

To determine if the binomial x-3 is a factor of the polynomial function f(x)=-5x^3+16x^2-9, we apply the Factor Theorem. If x-3 is indeed a factor, then the value of f(3) would be zero. Let's calculate f(3):

f(3) = -5(3)^3 + 16(3)^2 - 9
= -5(27) + 16(9) - 9
= -135 + 144 - 9
= 9 - 9
= 0

Since f(3) is zero, the binomial x-3 is indeed a factor of the polynomial function f(x).

Solution: Yes, x-3 is a factor of f(x).