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

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Solution

The correct option is D
10

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

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

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

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

$[∵ x + 1 = x - (- 1)]$

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

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

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

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