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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