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.
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