Division of a polynomial by a monomial

Division of a polynomial by a binomial by using long division

Division of a monomial by a monomial

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)?

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)?

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 ?

Every polynomial is a monomial.

Division of polynomial by using factorization

Can (y + 5) be the remainder on division of a polynomial f(y) by (y-2) ?