Question

Find remainder, if $f\left(x\right)=x^2-5x+6$ is divided by $x-5$.

Answer 1

Given that,

Polynomial $f\left(x\right)=x^2-5x+6$ is divided by $(x-5)$

To find out,

The remainder.

According to the remainder theorem, when a polynomial $f\left(x\right)$ is divided by $(x-a)$, the remainder is $f\left(a\right)$.

Hence, when $f\left(x\right)=x^2-5x+6$ is divided by $(x-5)$, the remainder is $f\left(5\right)$.

$f\left(5\right)=(5{)}^2-5(5)+6$

$=25-25+6$

$=6$

Hence, when $f\left(x\right)=x^2-5x+6$ is divided by $(x-5)$, the remainder is $6$.