Question

Let $f\left(x\right)=x^2+3x+2$. Then the remainder when $f\left(x\right)$ is divided by $(x-1)$ will be :

• A. $3$
• B. $5$
• C. $6$
• D. none of these

Answer 1

The correct option is C $6$

Let $f\left(x\right)=x^2+3x+2$.

The polynomial $f\left(x\right)$ is divided by $x-1$.

Then $x-1=0⟹x=1.$

By remainder theorem, the remainder is given by $f\left(1\right)$.
Hence, remainder of the given polynomial $f\left(x\right)$ is
$f\left(1\right)=(1{)}^2+3(1)+2=1+3+2=6$.
That is, the remainder obtained is $6$.

Hence, option $C$ is correct.