Question

Factorize: $x^4+x^2+1$

Answer 1

Factorize the Expression:

The given expression is,

$x^4+x^2+1=x^4+x^2+1+x^2-x^2$

$=x^4+2x^2+1-x^2$

$={\left(x^2+1\right)}^2-x^2$ $\left[\because {\left(a+b\right)}^2=a^2+2ab+b^2\right]$

$=(x^2+1+x)(x^2+1-x)$ $\left[\because a^2-b^2=(a+b)(a-b)\right]$

Hence the factors of $x^4+x^2+1$are $(x^2+1+x)$ and $(x^2+1-x).$