# Factorize x^4 + x^2 + 1

We have to factorise $x^{4} + x^{2} + 1$

### Solution

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

On adding and subtracting x2 to the given equation we get,

=$x^{4} + x^{2} + 1 + x^{2} – x^{2}$

by the identity $(a+b)^{2}= a^{2}+b^{2}+2ab$ we get

=$(x^{2}+1)^{2} – x^{2}$

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

Factors of $x^{4} + x^{2} + 1$ are $(x^{2}+1+x)(x^{2}+1-x)$