From the question, we were told that if f is a polynomial function and x - 5 is a factor of f. Then we should find f(5)
recall that, a function f can be simplified by it's root.
For instance, a second order function expressed by the equation below:
ax² + bx + c
a ≠ 0.
Can be expressed in function of it's roots x1, x2 such that:
ax² + bx + c = (x - x1) * (x - x2).
So, if x - 5 is a factor of f, this means that f can be expressed in function of x - 5,
that is, x = 5 is a roof of the equation.
This means that:
f(5) = 0