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

Answer 1

Answer:

(x - 3) is a factor of f(x)

Step-by-step explanation:

If (x - h) is a factor of f(x) then f(h) = 0 ← factor theorem

Thus if (x - 3) is a factor of f(x) then f(3) = 0

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

Thus (x - 3) is a factor of f(x)