AP Precalculus
~ 1.11: Rewriting Polynomials and Rational Functions ~
~ 1.11: Rewriting Polynomials and Rational Functions ~
Rewrite polynomial and rational expressions in equivalent forms.
Determine the quotient of two polynomial functions using long division.
Rewrite the repeated product of binomials using the binomial theorem.
The factored form of a polynomial or rational function readily provides information about real zeros; it can also reveal information about x-intercepts, asymptotes, holes, domain, and range.
The standard form of a polynomial or rational function can reveal information about end behaviors of the function.
The information extracted from different analytic representations of the same polynomial or rational function can be used to answer questions in context.
Polynomial long division is an algebraic process similar to numerical long division involving a quotient and remainder.
If the polynomial f is divided by the polynomial g , then f can be rewritten as f(x) = g(x)q(x) + r(x), where q is the quotient, r is the remainder, and the degree of r is less than the degree of g.
The result of polynomial long division is helpful in finding equations of slant asymptotes for graphs of rational functions.
Know how to use the binomial theorem to more easily expand certain expressions.
The video for AP Precalculus, 1.11: Polynomials and Complex Zeros will come out on Thursday, October 5, 2023.