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Factorisation Using Algebraic Identities

Factorize the...

Question

Factorize the following expression
$(x^{2} + 2 x + 1)$

(x + 1)^{2}

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(x - 1)^{2}

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(x + 1)^{3}

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None of these

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Solution

The correct option is A $(x + 1)^{2}$
Given,

$x^{2} + 2 x + 1$
split middle term i.e $2$
$= x^{2} + x      x + x + 1$ $1 + 1 = 2$
$1 + 1 = 2$
$x (x + 1) + (x + 1)$
$(x + 1) (x + 1)$
$= (x + 1)^{2}$ Ans

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Question :

One of the factors of x⁵+x+1 is

(1) 2x² - x - 1

(2) x³ - x²+ 1

(3) x² - 2x² + 1

(4) x³ + x² + 1

(x^{2} - x)^{2} - 8 (x^{2} - x) + 12

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