Question

Hello! I need some help with this homework question, please? The question is posted in the image below. Q13

Answer 1

If f is a polynomial function and x - 5 is a factor of f, then f(5) = 0

Step-by-step explanation

When a polynomial fraction is written in factored form,

`f(x)=a(x-x_1)(x-x_2)\ldots(x-x_n)`

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,

`f(x_1)=f(x_2)=\ldots=f(x_n)=0`

Hence, f(5) = 0 if x - 5 is a factor.