quick!! factorize x³ - 4x² + x + 6
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x³ - 4 x² + x + 6
==> x³ - 2 x² - 2 x² + x + 6 [ Split - 4 x² ]
==> x³ - 2 x² - ( 2 x² - x - 6 ) [ Take - 1 as common ]
==> x² ( x - 2 ) - ( 2 x² - 4 x + 3 x - 6 ) [ Take x² as common ]
==> x² ( x - 2 ) - [ 2 x ( x - 2 ) + 3 ( x - 2 ) ] [ Take commons ]
==> x² ( x - 2 ) - ( 2 x + 3 )( x - 2 )
==> ( x - 2 )( x² - 2 x - 3 ) [ x - 2 is common ]
==> ( x - 2 )( x² - 3 x + x - 3 ) [ Split and solve ]
==> ( x - 2 )( x ( x - 3 ) + 1 ( x - 3 ))
==> ( x - 2 )( x - 3 )( x + 1 )
The answer is ( x - 2 )( x - 3 )( x + 1 )
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