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Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm:
(i)
(ii)
(iii)
(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