Question

Find the factors of f(x), given that x = 4 is a zero.f(x) = x^3 − 7x^2 + 2x + 40 A. (x − 4)(x + 5)(x − 2)b. (x + 4)(x + 5)(x − 2)c. (x − 4)(x − 5)(x + 2)d. (x + 4)(x − 5)(x + 2)

Answer 1

Let's determine the factors of the following function:

$\text{f(x) = x}^3-7x^2\text{ + 2x + 40}$

Since one of the factors is given, which is x = 4 or (x - 4), let's determine the quadratic function using synthetic division.

We get,

$\text{f(x) = x}^3-7x^2+2x+40=(x-4)(x^2-3x-10)$$\text{ f(x) = (x - 4)(x + 2)(x - 5)}$

Therefore, the answer is letter C : (x - 4)(x - 5)(x + 2)