ANSWER
If f is a polynomial function and x - 5 is a factor of f, then f(5) = 0
EXPLANATION
When a polynomial fraction is written in factored form,
[tex]f(x)=a(x-x_1)(x-x_2)\ldots(x-x_n)[/tex]
The values in the factors, x₁, x₂, ..., xₙ are the zeros of the polynomial - also known as roots or x-intercepts.
This means that f evaluated in any of these zeros, the value of the function is zero,
[tex]f(x_1)=f(x_2)=\ldots=f(x_n)=0[/tex]
Hence, f(5) = 0 if x - 5 is a factor.
