Question

Factorize: x⁴ + x² + 25.

Answer 1

The given expression to be factorized is  x⁴ + x² + 25

This can be written in the form

x⁴ + x² + 25= ` (x^2)^2 + 2x^2 .5 + (5)^2 - 9x^2`

                  ` = {(x^2)^2 + 2x^2 .5 + (5)^2}- (3x)^2`

                  ` = (x^2 + 5)^2 - (3x)^2`

` = (x^2 + 5 + 3x) (x^2 + 5 - 3x)`

We cannot further factorize the expression. 

So, the required factorization is. `x^4  + x^2 + 25 = (x^2 + 5+3x)(x^2 + 5 - 3x)`