Question

The factors of x⁴ + x² + 25 are

Options

• (x² + 3x + 5) (x² − 3x + 5)

• (x² + 3x + 5) (x² + 3x − 5)

• (x² + x +5) (x² − x + 5)

• none of these

Answer 1

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

This can be written in the form

`x^4 + x^2 + 25 = (x^2)^2+ 2.x^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)^2 - (3x)^2`

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