Factorise (x²-2x)²+11(x²-2x)+24
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( x² - 2x )² - 11 ( x² - 2x ) + 24
Let a = ( x² - 2x )
= y² - 11y + 24
= y² - 8y - 3y + 24
= y ( y - 8 ) -3 ( y - 8)
= ( y - 8 ) ( y - 3 )
Putting value of y
= ( x² - 2x - 8 ) ( x² - 2x - 3 )
= ( x² - 4x + 2x - 8 ) ( x² - 3x + 1x - 3)
= [ x ( x- 4 ) +2 ( x - 4 ) ] [x ( x - 3 ) +1 ( x - 3 )]
= ( x - 4 ) ( x + 2 ) ( x - 3 ) ( x + 1 )
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