Answer
The given statement is true.
Work Step by Step
Consider the statement:
If $p\left( 3 \right)=0$ for some polynomial $p\left( x \right)$ then $x-3$ is a factor of $p\left( x \right)$.
The remainder theorem is explained as:
When the function $P\left( x \right)$ is divided by $x-r$ then the remainder is $P\left( r \right)$.
From the remainder theorem, it can be noticed that the remainder is denoted by $P\left( r \right)$.
If $p\left( 3 \right)=0$ for some polynomial $p\left( x \right)$, it says that the remainder obtained is 0 when $p\left( x \right)$ is divided by $x-3$.
Since the remainder is 0, $x-3$ is a factor of $p\left( x \right)$.
Therefore, the given statement is true.
