Factorize 1- 1 x - 1 x 2 - 1 x 3

1 + 1x + 1x^2 + 1x^3 = ( 1 + 1x) + 1x^2( 1 + 1x) = ( 1 + 1x)( 1 + 1x^2) ...

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Byju's Answer

Standard VIII

Mathematics

Addition and Subtraction of Algebraic Expression

Factorize 1...

Question

Factorize $(1 + \frac{1}{x} + \frac{1}{x^{2}} + \frac{1}{x^{3}})$

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Solution

$1 + \frac{1}{x} + \frac{1}{x^{2}} + \frac{1}{x^{3}}$
$= (1 + \frac{1}{x}) + \frac{1}{x^{2}} (1 + \frac{1}{x})$
$= (1 + \frac{1}{x}) (1 + \frac{1}{x^{2}})$

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Similar questions

Q. Resolve into factors

x^{3} + x^{2} - \frac{1}{x^{2}} + \frac{1}{x^{3}}

(x+1) is a factor of the polynomial
(a) $x^{3} + x^{2} - x + 1$
(b) $x^{3} + 2 x^{2} - x - 2$
(c) $x^{3} + 2 x^{2} - x + 2$
(d) $x^{4} + x^{3} + x^{2} + 1$

Q. Factors of

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

(x + 1)

is the only factor of

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

Q. Question 13
x + 1 is a factor of the polynomial

A)

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

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

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

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

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Factorize (1+1x+1x2+1x3)

1+1x+1x2+1x3=(1+1x)+1x2(1+1x)=(1+1x)(1+1x2)

Factorize $(1 + \frac{1}{x} + \frac{1}{x^{2}} + \frac{1}{x^{3}})$

$1 + \frac{1}{x} + \frac{1}{x^{2}} + \frac{1}{x^{3}}$
$= (1 + \frac{1}{x}) + \frac{1}{x^{2}} (1 + \frac{1}{x})$
$= (1 + \frac{1}{x}) (1 + \frac{1}{x^{2}})$