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  • Factorise : (iv) 2 y ^3 + y ^2 - 2y - 1

Factorise :  2y^3 + y^2 - 2y - 1

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Solution

Given polynomial is  2y^3 + y^2 - 2y - 1
Now, by hit and trial method we observed that  (y-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
2y^3 + y^2 - 2y - 1= (y-1)(2y^2+3y+1)
 = (y-1)(2y^2+2y+y+1)    
 = (y-1)(2y+1)(y+1)
Therefore, on factorization of  2y^3 + y^2 - 2y - 1 we will get  (y-1)(2y+1)(y+1)

Posted by

Gautam harsolia

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