Question

If f is a polynomial function and xminus−5 is a factor of​ f, then ​f(5)equals=​_______.

Answer 1

if (x - 5 ) is a factor of f(x ) then x = 5 is a root of f(x) and f(5) = 0

Answer 2

Answer:

$f(5) = 0$

Step-by-step explanation:

A function $f$ can be simplified by it's roots.

For example, a second order function expressed by the following equation:

$ax^{2} + bx + c, a\neq0.$

Can be expressed in function of it's roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = (x - x_{1})*(x - x_{2})$.

Is $x-5$ is a factor of f, this means that f can be expressed in function of $x - 5$, that is, x = 5 is a root of the equation.

This means that:

$f(5) = 0$