Question

If the expression $x^2-x+c$ when divided by $(x+1)$ leaves a remainder $3$, find ${}^{\prime }c$

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (B)

$1$

Remainder theorem says that when $p\left(x\right)$ is divided by $(x-a)$ the remainder is given by $p\left(a\right)$

Let $p\left(x\right)=x^2-x+c$

It is given that the expression $p\left(x\right)$ when divided by $(x+1)$ leaves a remainder $3$

Using Remainder theorem, we have

$Remainder=f(-1)=1-(-1)+c=3$

$\Rightarrow c=1$