Question
Factorise$ : x^4+ x^2+ 1$
✓
Answer
$x^4+ x^2+ 1$
$= x^4 + 2x^2 + 1 - x^2$
$= (x^2)^2 + 2x^2 + (1)^2 - x^2$
$= ( x^2 + 1 )^2 - (x)^2 [ \because a^2 - b^2 = ( a + b )( a - b )]$
$= ( x^2 + 1 - x )( x^2 + 1 + x )$
$= x^4 + 2x^2 + 1 - x^2$
$= (x^2)^2 + 2x^2 + (1)^2 - x^2$
$= ( x^2 + 1 )^2 - (x)^2 [ \because a^2 - b^2 = ( a + b )( a - b )]$
$= ( x^2 + 1 - x )( x^2 + 1 + x )$
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