The **Polynomial Remainder Theorem** states that the remainder of the division of a polynomial $f(x)$ by a linear polynomial $x - r$ is equal to $f(r)$. In particular, $x-r$ divides $f(x) \iff f(r)=0$
I have the following problem related to the above result:
Given a polynomial function [math]f(x)= ax+b[/math]
where $a,b$ are integers and $x$ is an integer variable. Assuming that there exist a single value of $x$ called $c$ such that $c-r$ divide $ac+b$
Then I am asking if one can deduce that $f(r)=0$. The reason for this question is based on the fact that the **Polynomial Remainder Theorem** is valid only when $x$ is a variable.
I have the following problem related to the above result:
Given a polynomial function [math]f(x)= ax+b[/math]
where $a,b$ are integers and $x$ is an integer variable. Assuming that there exist a single value of $x$ called $c$ such that $c-r$ divide $ac+b$
Then I am asking if one can deduce that $f(r)=0$. The reason for this question is based on the fact that the **Polynomial Remainder Theorem** is valid only when $x$ is a variable.
