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

`f(5) = 0`

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\\eq0.`

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`