Question

How do you factor $x^2+1$?

Answer 1

Find the factor of ${\mathit{x}}^{\mathbf{2}}\mathbf{+}\mathbf{1}$.

Given, the expression is $x^2+1$.

$x^2+1$ can be framed as $x^2-(-1)$.

$x^2-(-1)$ is in the form of $a^2-b^2$, where,$a^2-b^2=(a-b)(a+b)$

Assume that $(-1)$ as $i^2$.

So,$x^2-(-1)=x^2-i^2$

From above identity,

Factors of $x^2+1$ is $(x-i)(x+i)$.

Therefore, the factor of $x^2+1$is $(x-i)(x+i)$.