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Factors of Algebraic Expressions and Factorisation

Factorise: x...

Question

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

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Solution

$= x^{4} + 2 \times x^{2} + 1 - x^{2}$

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

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

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

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