Find - x4-3x2-2x-3x-2

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Standard IX

Mathematics

Long Division Method to Divide Two Polynomials

Find : x4-3...

Question

Find :
$\frac{x^{4} - 3 x^{2} - 2 x - 3}{(x - 2)}$

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Solution

We divide $x^{4} - 3 x^{2} - 2 x - 3$ by $(x - 2)$ as shown in the above image:

From the division, we observe that the quotient is $x^{3} + 2 x^{2} + x$ and the remainder is $- 3$ .

Hence, the quotient is $x^{3} + 2 x^{2} + x$ and the remainder is $- 3$ .

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Similar questions

Q. The remainder obtained when the polynomial

x^{4} - 3 x^{2} - 2 x - 3

is divided by x-2 is

Find in each case, the remainder when
(i) $x^{4} - 3 x^{2} + 2 x + 1$ is divided by x - 1
(ii) $x^{3} + 3 x^{2} - 12 x + 4 i s d i v i d e d b y x - 2$
(iii) $x^{4} + 1 i s d i v i d e d b y x + 1.$

Q. Differentiate with respect to x

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

Q. Let

f (x) = ln x

and

g (x) = (\frac{x^{4} - x^{3} + 3 x^{2} - 2 x + 2}{2 x^{2} - 2 x + 3)})

. The domain of

f (g (x))

Q. Find, in each case, the remainder when:

x^{4} - 3 x^{2} + 2 x + 1

is divided by

x - 1

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Find : x4−3x2−2x−3(x−2)

We divide x4−3x2−2x−3 by (x−2) as shown in the above image:From the division, we observe that the quotient is x3+2x2+x and the remainder is −3.Hence, the quotient is x3+2x2+x and the remainder is −3.

Find :
$\frac{x^{4} - 3 x^{2} - 2 x - 3}{(x - 2)}$

We divide $x^{4} - 3 x^{2} - 2 x - 3$ by $(x - 2)$ as shown in the above image:

From the division, we observe that the quotient is $x^{3} + 2 x^{2} + x$ and the remainder is $- 3$ .

Hence, the quotient is $x^{3} + 2 x^{2} + x$ and the remainder is $- 3$ .