Question

Factorise: x⁴ - 3x² + 2​

Answer 1

Assume x² be x.

Then,

${x}^{4} - {3x}^{2} + 2 = {x}^{2} - 3x + 2$

Now,

${ \huge{ \boxed{ {x}^{2} - 3x + 2 }}} \\ \\ { \huge{ \boxed{ {x}^{2} - 2x - x + 2 }}} \\ \\ { \huge{ \boxed{ x(x - 2) - 1(x - 2) }}} \\ \\ { \huge{ \boxed{(x - 2)(x - 1)}}}$

Hence, Putting x² at the place of x in the terms above, we get,

${ \large{(x - 2)(x - 1) = ( {x}^{2} - 2 )( {x}^{2} - 1 )}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = { \red{ \large{[(x - \sqrt{2} )(x + \sqrt{2} )][(x + 1)(x - 1)]}}}$