The Intermediate Value Theorem
If P(x) defines a polynomial function with only real coefficients, and if, for real numbers a and b, the values P(a) and P(b) are opposite in sign, then there exists at least one real zero between a and b. Division Algorithm for Polynomials
Let P(x) and is D(x) be two polynomials, with the degree
of D(x) greater than zero and less than the degree of P(x).
Then there exist unique polynomials Q(x) and R(x) such
that
where either R(x) = 0 or the degree of R(x) is less than the
degree of D(x).
