Question

What will be the remainder when $4x^4-3x^3+2x^2-x$ is divided by $x+1$?

• A. 1
• B. 0
• C. 7
• D. 10

Answer 1

The correct option is D

10

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

To find the remainder of $\frac{4x^4-3x^3+2x^2-x}{x+1}$,
we will use remainder theorem.

Remainder of $\frac{p\left(x\right)}{x-a}$ is $p\left(a\right)$.

$\Rightarrow$ Remainder of $\frac{4x^4-3x^3+2x^2-x}{x+1}$ is $p(-1)$.

$[\because x+1=x-(-1\left)\right]$

$p(-1)=4(-1{)}^4-3(-1{)}^3+2(-1{)}^2-(-1)$

$\Rightarrow p(-1)=4+3+2+1=10$

Hence, the remainder of $\frac{4x^4-3x^3+2x^2-x}{x+1}$ is 10.