of a polynomial of degree greater than four can be obtained, even though that is not always possible. For example, if the rational root theorem can be used to obtain a single (rational) root of a quintic polynomial, it can be factored out to obtain a quartic (fourth degree) quotient; the explicit formula for the roots of a quartic polynomial can then be used to find the other four roots of the quintic. Finding tangents to polynomial functions Polynomial long division can be used to find the equation of the line that is tangent to the graph of the function defined by the polynomial P(x) at a particular point If R(x) is the remainder of the division of P(x) by then the equation of the tangent line at to the graph of the function is regardless of whether or not r is a root of the polynomial. Example Find the equation of the line that is tangent to the following curve at : Begin by dividing the polynomial by : The tangent line is . Cyclic redundancy check A cyclic redundancy check uses the remainder of polynomial division to detect errors in transmitted messages. See also Polynomial remainder theorem Synthetic division, a more concise method of performing Euclidean polynomial division Ruffini's rule Euclidean domain Gröbner basis Greatest common divisor of two polynomials References Polynomials Computer algebra Division (mathematics)