Question

One of the zeros of the following polynomial function is 5. f(x) = x^4 - 4x^3 - 6x^2 + 4x + 5. What is the factored form of the function?

a) f(x) = (x - 5)(x^3 - x^2 - 11x - 1)
b) f(x) = (x - 5)(x^3 - 2x^2 - 12x - 5)
c) f(x) = (x - 5)(x^3 - 3x^2 - 13x - 7)
d) f(x) = (x - 5)(x^3 - 4x^2 - 14x - 9)

Answer 1

The factored form of the function is f(x) = (x - 5)(x^3 + x^2 - 7x - 1).

Step-by-step explanation:

To find the factored form of the function, we need to determine the other zeros. Since we are given that one of the zeros is 5, we can apply synthetic division with 5 as the divisor. Performing synthetic division, we get: (x - 5)(x^3 + x^2 - 7x - 1). Therefore, the factored form of the function is: f(x) = (x - 5)(x^3 + x^2 - 7x - 1).