Question

Write the remainder when the polynomial $f\left(x\right)=x^3+x^2-3x+2$ is divided by $x+1$.

Answer 1

Given: $f\left(x\right)=x^3+x^2-3x+2$ is divided by 𝑥+1

We know by remainder theorem that if 𝑓(𝑥) is divided by polynomial $(x+a)$ then, remainder $=f(-a)$

$\therefore$ Remainder $=f(-1)$

$=(-1{)}^3+(-1{)}^2-3\times (-1)+2$

$=-1+1+3+2$

$=5$

Hence, the remainder is 5.