Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in each of the following:
(i) 
(ii) 
(iii) 
(iv) 
(i) 
and 
Degree of 
; therefore degree of 
and degree of remainder is less than 2,
Let 
and 
By applying division algorithm:
Dividend = Quotient× Divisor + Remainder
On substituting values in the above relation we get,
On comparing coefficients we get,
On solving above equations we get,
, 
, 
, 
On substituting these values for 
(ii) 
and 
Degree of 
; therefore degree of 
and degree of remainder is less than 2.
Let 
and 
By applying division algorithm:
Dividend = Quotient× Divisor + Remainder
On substituting values in the above relation we get,
On comparing coefficients we get,
On solving above equations we get,
, 
, 
, 
; 
On substituting these values for 
(iii) 
and 
Degree of 
; therefore degree of 
and degree of remainder is less than 2,
Let 
and 
By applying division algorithm:
Dividend = Quotient× Divisor + Remainder
On substituting values in the above relation we get,
On comparing coefficients we get,
On solving above equations we get,
, 
, 
, 
On substituting these values for 
(iv) 
and 
Degree of 
; therefore degree of 
and degree of remainder is less than 2,
Let 
and 
By applying division algorithm:
Dividend = Quotient× Divisor + Remainder
On substituting values in the above relation we get,
On comparing coefficients we get,
On solving above equations we get,
, 
, 
, 
On substituting these values for 
