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Answer the following and justify. (i) ...

Answer the following and justify.
(i) can `x^(2)-1` be the quotient on division of `x^(6) +2x^(3) +x - 1` by a polynomial in x of degree 5?
(ii) What will be quotient and remainder be on division of `ax^(2)+bx +c` by `px^(3) +qx^(2) +rx +s, p ne 0`?
(iii) If on division of a polynomial `p(x)` by a polynomial `g(x)`, the quotient is zero, what is the relation between the degree of `p(x)` and `g(x)`?
(iv) If on division of a non-zero polynomial `p(x)` by a polynomial `g(x)`, the remainder is zero, what is the relation between the degrees of `p(x)` and `g(x)`?
(v) Can be quadratic polynomial `x^(2) +kx +k` have equal zeroes for some odd integer `k gt 1`?

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