Question

Using the factor theorem, which of the following is a factor of the polynomial function f(x)=4x^3 −8x^2 −60x?

a) x−3
b) x^4
c) x−5
d) x^5

Answer 1

Using the factor theorem, we find that the correct answer is option c) x-5, which is a factor of the polynomial function f(x)=4x^3 −8x^2 −60x because when x=5 is substituted into the function, the result is zero.

Step-by-step explanation:

The student asked to use the factor theorem to find which of the given options is a factor of the polynomial function f(x)=4x3 −8x2 −60x. We need to substitute x with the value from each option and check if f(x) equals zero. If so, that option is a factor of the polynomial.

1. For option a, (x−3), we check f(3): f(3) = 4(3)3 − 8(3)2 − 60(3) which does not equal zero. So, this is not a factor.
2. Option b, x4, and option d, x5, are not linear factors and therefore not applicable for this function.
3. For option c, (x−5), we check f(5): f(5) = 4(5)3 − 8(5)2 − 60(5) = 500 − 200 − 300 = 0. Since f(5) equals zero, x−5 is a factor of the polynomial.

Therefore, the correct answer is option c) x−5.