Question

factorisr :- x to the power 4 + x square + 1

Answer 1

given,
${x}^{4} + {x}^{2} + 1$
we will use the first identity for this
$which \: is \: ( {a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$

therefore,

${ ({x}^{2}) }^{2} + 2( {x}^{2})(1) + {1}^{2}$
one thing to keep in mind,

1 square is also one an 1 root of 1 is also one

therefore we have,
${ ({x}^{2} + 1) }^{2} \\ or \\ ( {x}^{2} + 1)( {x}^{2} + 1)$
is the factorization

Answer 2

See the attached picture.