Let's determine the factors of the following function:
[tex]\text{f(x) = x}^3-7x^2\text{ + 2x + 40}[/tex]
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,
[tex]\text{f(x) = x}^3-7x^2+2x+40=(x-4)(x^2-3x-10)[/tex][tex]\text{ f(x) = (x - 4)(x + 2)(x - 5)}[/tex]
Therefore, the answer is letter C : (x - 4)(x - 5)(x + 2)
