Q. 2

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm:

(i)

(ii)

(iii)

Answer :

(i) and


Degree of ; therefore degree of and degree of remainder is of degree 1 or less,


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



Since remainder is zero, therefore


(ii) and


Degree of ; therefore degree of and degree of remainder is of degree 1 or less,


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



Since remainder is 2, therefore


(iii) and


Degree of ; therefore degree of and degree of remainder is of degree 2 or less,


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



Since remainder is , therefore


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