Factorize $x^4+ x^2 + 1$ to two quadratic factors.

Given: Polynomial $x^4+ x^2 + 1$

To do: To factorize the given polynomial into two quadratic factors.

Solution:

 $\Rightarrow f(x) = x^4 + x^{2} + 1$ 

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

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

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

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

Updated on: 10-Oct-2022

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