Question

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Answer 1

Answer:
Factor x^8+x^4+1

Rewrite the middle term.
X^8+2x^4.1-x^4+1

Rearrange terms.
x^8+2x^4.1+1 -x^4
Factor first three terms by perfect square rule
(X^4+1)^2-x^4
Rewrite
x^4
as
(X^2)^2
(X^4+1)-(x^2)^2
Since both terms are perfect squares, factor using the difference of squares formula,
a^2-b^2=(a+b)(a-b)
where
a=x^4+1
and
b=x^2

Simplify.
(X^4+1+x^2)(x^4+1-x^2)
Explanation:

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Answer 2

given:

`{x}^(8) + {x}^(4) + 1`

to find:

factorise

solution:

`{x}^(8) + {x}^(4) + 1`

`= x ^(8) + 2 {x}^(4) + 1 - {x}^(4)`

`= ( {x}^(4) + 1 {)}^(2) - ( {x}^(2) {)}^(2)`

`= ({x}^(4 ) + 1 + {x}^(2)) ( {x}^(4) + 1 - {x}^(2) )`

`= ( {x}^(4) + 2 {x}^(2) + 1 - {x}^(2) )( {x}^(4) - {x}^(2) + 1)`

`= (( {x}^(2) + 1 {)}^(2) - {x}^(2) )( {x}^(4) - {x}^(2) + 1)`

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

`= ( {x}^(4) - {x}^(2) + 1)`