x³-2x²-x+2. Factorize it.
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(x^2-1) (x-2) is your answer
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Solution :
x³ - 2x² - x + 2
= x²( x - 2 ) - 1( x - 2 )
= ( x - 2 )( x² - 1 )
= ( x - 2 )( x² - 1² )
= ( x - 2 )( x + 1 )( x - 1 )
[ Since , a² - b² = ( a + b )( a - b ) ]
Therefore ,
x³ - 2x² - x + 2 = ( x - 1 )( x - 2 )( x + 1 )
••••
x³ - 2x² - x + 2
= x²( x - 2 ) - 1( x - 2 )
= ( x - 2 )( x² - 1 )
= ( x - 2 )( x² - 1² )
= ( x - 2 )( x + 1 )( x - 1 )
[ Since , a² - b² = ( a + b )( a - b ) ]
Therefore ,
x³ - 2x² - x + 2 = ( x - 1 )( x - 2 )( x + 1 )
••••
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