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




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