AP Precalculus

1.11 Course Objectives

• 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.

1.11 Key Knowledge

• 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.

Video

• The video for AP Precalculus, 1.11: Polynomials and Complex Zeros will come out on Thursday, October 5, 2023.