Using division algorithm, find the quotient and remainder on dividing f(x) by g(x) where $f (x) = 6 x^{3} + 13 x^{2} + x - 2 a n d g (x) = 2 x + 1.$

Open in App

Solution

Given, $f (x) = 6 x^{3} + 13 x^{2} + x - 2$
and g(x) = 2x + 1,
$f (x) \div g (x) \Rightarrow 2 x + 1) ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 6 x^{3} + 13 x^{2} + x - 2 (3 x^{2} + 5 x - 2$
$6 x^{3} + 3 x^{2}$
$- -$
$- ------------------- -$
$10 x^{2} + x - 2$
$10 x^{2} + 5 x$
$- -$
$¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯$
$- 4 x - 2$
$- 4 x - 2$
$+ +$
$¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯$
$0$
quotient $= 3 x^{2} + 5 x - 2,$ remainder = 0

Suggest Corrections

Similar questions

f (x)

g (x)

f (x) = x^{4} - 5 x + 6, g (x) = 2 - x^{2}

f (x) = 10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3

g (x) = 2 x^{2} - x + 1

f (x) =

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

g (x) =

2 x + 2

\frac{f (x)}{g (x)}

In each of the following, using the remainder Theorem, find the remainder when f(x) is divided by g(x) and verify the result y actual division.

f(x) = $2 x^{4} - 6 x^{3} + 2 x^{2} - x + 2$ , g(x) = x + 2

Join BYJU'S Learning Program