(i) Can be the quotient on division of
by a polynomial in of degree ?
(ii) What will the quotient and remainder be on
division of by
3 2
px qx rx s, p 0
?
(iii) If on division of a polynomial by a
polynomial , the quotient is zero, what is
the relation between the degrees of and
?
(iv) If on division of a non-zero polynomial by
a polynomial , the remainder is zero, what
is the relation between the degrees of and
?
(v) Can the quadratic polynomial have
equal zeroes for some odd integer ?
Solution
(i) No.
When you divide the polynomial
by a polynomial of degree 2, then the degree of
the polynomial of quotient is 4.
By the division algorithm,