Question

divide and verify x+3xsq-1 by 1-x

Answer 1

Heya !!




F ( X ) = X + 3X² - 1



=> 3X² + X - 1



And,


G ( X ) = 1 - X = - X + 1



On dividing F(X ) by G ( X ) , we get




- X +1 ) 3X² + X - 1 ( - 3X - 4


********3X² - 3X


-----------------------------------


************** + 4X - 1



******************4X² - 4


------------------------------------------

Remainder = 3




And,


Quotient = -3X - 4





Verifying,





We know that,



Dividend = Divisor × Quotient + Remainder




Dividend = ( - X + 1 ) × ( -3X - 4 ) + 3




Dividend = -X ( -3X - 4 ) +1 ( -3X -4 ) + 3




Dividend = 3X² + 4X - 3X - 4 + 3





Dividend = 3X² + X - 1.