Question

Using the factor theorem, which of the following is a factor of the polynomial function f(x)=5x^3 −5x^2 −60x?

a) x−4
b) x^4
c) x−3
d) x^5

Answer 1

The factor theorem can be used to find factors of a polynomial function by substituting values from the options and checking for a result of 0.

Step-by-step explanation:

The factor theorem states that if a polynomial f(x) has a factor (x - a), then f(a) = 0. To determine which of the given options is a factor of the polynomial function f(x) = 5x^3 - 5x^2 - 60x, we need to substitute the values from the options into the polynomial and check which one gives a result of 0.

Let's test each option:

a) x - 4:

f(4) = 5(4)^3 - 5(4)^2 - 60(4) = 320 - 80 - 240 = 0

Since f(4) = 0, option a) x - 4 is a factor of the given polynomial function.

Answer: a) x - 4