Question

1. Factorize the following question.

x⁴+x²+1 ​

Answer 1

Answer:

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Answer 2

$\begin{gathered}\Large{\bold{\pink{\underline{Formula \: Used \::}}}} \end{gathered}$

$(1). \: \boxed{ \pink{\tt \: {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}}}$

$(2). \: \boxed{ \pink{\tt \: (x - y)(x + y) = {x}^{2} \: - \: {y}^{2}}}$

$\large\underline\purple{\bold{Solution :- }}$

$\rm :\implies\: {x}^{4} + {x}^{2} + 1$

$\longmapsto\red{\boxed{\tt \: Adding \: and \: subtracting \: {x}^{2}}}$

$\rm :\implies\: {x}^{4} + {x}^{2} + 1 + {x}^{2} - {x}^{2}$

$\rm :\implies\: {x}^{4} + {2x}^{2} + 1 - {x}^{2}$

$\rm :\implies\: {( {x}^{2} + 1)}^{2} - {x}^{2}$

$\bf :\implies\: ({x}^{2} + 1 + x)( {x}^{2} + 1 - x)$