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Mathematics Polynomials

Answer the following and justify: (i) Can x^2 - 1 be the quotient on division of x^6 + 2x^3 + x - 1 by a poly…

Answer the following and justify:
  1. (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?
  2. (ii)What will the quotient and remainder be on division of ax^2 + bx + c by px^3 + qx^2 + rx + s, p not equal to 0?
  3. (iii)If on division of a polynomial p(x) by a polynomial g(x), the quotient is zero, what is the relation between the degrees of p(x) and g(x)?
  4. (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)?
  5. (v)Can the quadratic polynomial x^2 + kx + k have equal zeroes for some odd integer k > 1?

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