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Factorise : (i) x ^3 - 2x ^2 - x + 2

5.(i) Factorise :

   (i)    x^3 - 2x^2 - x +2

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Given polynomial is  x^3 - 2x^2 - x +2

Now, by hit and trial method we observed that  (x+1)  is one of the factors of the given polynomial.

By long division method, we will get


We know that  Dividend = (Divisor \times Quotient) + Remainder

 x^3 - 2x^2 - x +2 = (x+1)(x^2-3x+2)+0

                                       = (x+1)(x^2-2x-x+2)
             
                                       = (x+1)(x-2)(x-1)

Therefore, on factorization of  x^3 - 2x^2 - x +2 we will get  (x+1)(x-2)(x-1)
 

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