Which of the following is a factor of $f( x)=x^{2}-9 x+20?$
$A).\ ( x-2)$
$B).\ ( x-3)$
$C).\ ( x-4)$
$D).\ ( x-5)$

Given: Polynomial: $f( x)=x^{2}-9 x+20$

To do: To find the factor of the given polynomial.

Solution:

Given polynomial: $f( x)=x^{2}-9 x+20$

Let $x-2=0\Rightarrow x=2$, Put this value in $f( x)$.

$f( 2)=2^2-9( 2)+20$

$=4-18+20$

$=6$

So, $( x-2)$ is not a factor of $f( x)=x^{2}-9 x+20$.

Let $( x-3)=0\Rightarrow x=3$, Put this value in $f( x)$.

$f( 3)=3^2-9( 3)+20$

$=9-27+20$

$=29-27$

$=2$

So $( x-3)$ is also not a factor of $f( x)=x^{2}-9 x+20$.

Let $( x-4)=0\Rightarrow x=4$, Put this value in $f( 4)$.

$f( 4)=4^2-9( 4)+20$

$=16-36+20$

$36-36$

$=0$

Therefore, $( x-4)$ is a factor of $f( x)=x^{2}-9 x+20$. 

Thus, option $( C)$ is correct.