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Factorise : (ii) x^3 - 3x ^2 - 9x - 5

5.(ii) Factorise :

   (ii)    x^3 - 3x^2 -9x -5

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Given polynomial is  x^3 - 3x^2 -9x -5

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

By long division method, we will get


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

 x^3 - 3x^2 -9x -5=(x+1)(x^2-4x-5)

                                       = (x+1)(x^2-5x+x-5)
             
                                       = (x+1)(x-5)(x+1)

Therefore, on factorization of  x^3 - 3x^2 -9x -5 we will get  (x+1)(x-5)(x+1)

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