Question

Please answer :-Factorize x²+1.

Answer 1

The given expression is

$x^2+1$

We can not factorize this expression bt the normal factorizing ways

Because it is a binomial with + as a middle sign can not be distributed into 2 factors

Then there is no factorizing for the given binomial

If the sign between the two terms is (-), then we can factorize it into two same factors with different middle sign

We can use the complex numbers to factorize it

$\begin{gathered} x^2=(x)(x) \\ 1=(i)(-i) \\ (x)(i)+(x)(-i)=(xi)-(xi)=0 \\ (x+i)(x-i) \end{gathered}$

Then the factors are (x + i) and (x - i)

$x^2+1=(x+i)(x-i)$