Algebra 89 - Multiplying Polynomial Functions @MyWhyU

Uploaded August 2021 | Updated September 2026, 2 weeks ago

In the previous lecture we saw how polynomial functions could be added or subtracted, producing new polynomial functions with different characteristics. In this lecture we will see how to multiply polynomial functions and show how the resulting function's characteristics are related to the polynomials that were multiplied.

Algebra 89 - Multiplying Polynomial Functions

$Algebra 91 - Rational Functions and Vertical Asymptotes A rational function is any function that can be written as a fraction whose numerator and denominator are polynomials. Rational functions include a broad range of possibilities. For example, since a polynomial can be a constant, a rational functions numerator and denominator can both be constants, in which case the rational function is simply a constant function. Unlike polynomial functions whose domains include all real numbers, in this lecture we show that any x value that causes the functions denominator to be zero will be excluded from the functions domain. These excluded x values produce missing points in the functions graph, and these missing points may be the locations of vertical asymptotes. Even though a functions graph can approach infinitely close to a vertical asymptote, it can never intersect that asymptote, since when the denominators value is zero, the functions value is undefined. A vertical asymptote is therefore a vertical line that a functions graph can approach arbitrarily close to, but can never intersect.$ $Pre-Algebra 14 - Creating Common Denominators Addition and subtraction of fractions with different denominators requires creating a common denominator. Using the number line, this mysterious process can be easily visualized.$

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