Question

factorise (x^2-2x)^2 - 23(x^2) + 120

Answer 1

Answer:

( x² - 2x )² - 23(x² - 2x ) + 120

Let a = x² - 2x

= a² - 23a + 120

= a² -15a - 8a + 120

= a( a - 15 ) - 8 ( a - 15 )

= ( a - 15 )( a - 8 )

= ( x² - 2x - 15 ) ( x² - 2x - 8 )

= [ x2 + 3x - 5x - 15 ] ( x² -4x + 2x - 8 )

= [ x ( x + 3 ) - 5 ( x + 3 ) ] [ x ( x - 4 ) + 2(x - 4 )]

= ( x + 3 )( x - 5 ) ( x - 4 ) ( x + 2 )

= ( x - 5 ) ( x - 4 ) ( x + 2 ) ( x + 3 )

I hope this helps you.