Question

Find the remainder when $p\left(x\right)=x^2+3x+4$ is divided by $x+1$.

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is C $2$

$p\left(x\right)=x^2+3x+4=(x+1)(x+2)+2$

Dividing $p\left(x\right)$ with $x+1$

$\Rightarrow \frac{(x+1)(x+2)+2}{x+1}$

$\Rightarrow \frac{(x+1)(x+2)}{x+1}+\frac{2}{x+1}$

$\Rightarrow (x+2)+\frac{2}{x+1}$

$\Rightarrow$ remainder$=2$