Divide $x^{6} - 2 x^{5} - x + 2$ by $x - 2$

Open in App

Solution

Dividend is rewritten as $x^{6} - 2 x^{5} + 0 . x^{4} + 0. x^{3} + 0. x^{2} - x + 2$
Now, by synthetic division
$∴$ the quotient is $x^{5} - 1$ and remainder is $0$ .

Suggest Corrections

Similar questions

Q. When the polynomial

x^{6} - 2 x^{5} + 3 x^{2} + 4

is divided by

x + 1

the remainder is :

Q. If

lim x \to - \infty (\sqrt{x^{6} + a x^{5} + b x^{3} - c x + d -} \sqrt{x^{6} - 2 x^{5} + x^{3} + x + 1}) = 2

then

Find the coefficient of $x^{90}$ in $(x + x^{2} + x^{3} + . . . . . . . . . .)^{2} (x^{5} + x^{6} + . . . . . . . . . . .)^{9}$

You are given
$cos x = 1 - \frac{x^{2}}{2!} + \frac{x^{4}}{4!} - \frac{x^{6}}{6!} . . . . . .$ ;
$sin x = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - \frac{x^{7}}{7!} . . . . . .$ ;
$tan x = x + \frac{x^{3}}{3} + \frac{2 x^{5}}{15} . . . . . .$
Then the value of
$lim x \to 0 \frac{x cos x + sin x}{x^{2} + tan x}$ is

___

Q. Find the quotient and remainder when

3 x^{7} - x^{6} + 31 x^{4} + 21 x + 5

is divided by

x + 2

Join BYJU'S Learning Program

Divide x6−2x5−x+2 by x−2

Dividend is rewritten as x6−2x5+0.x4+0.x3+0.x2−x+2Now, by synthetic division∴ the quotient is x5−1 and remainder is 0.

Divide $x^{6} - 2 x^{5} - x + 2$ by $x - 2$

Dividend is rewritten as $x^{6} - 2 x^{5} + 0 . x^{4} + 0. x^{3} + 0. x^{2} - x + 2$
Now, by synthetic division
$∴$ the quotient is $x^{5} - 1$ and remainder is $0$ .