Question

factorize the term=x⁴+x^2+1



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Answer 1

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

$= { ({x}^{2} )}^{2} + {x}^{2} + {1}^{2}$

Add and Subtract $x^2$

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

By Using,

${a}^{2} + 2ab + {b}^{2} = (a + b) ^{2}$

We get,

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

By Using,

${a}^{2} - {b}^{2} = (a + b)(a - b)$

We get,

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