Mary Jane Sterling - Pre-Calculus - 1001 Practice Problems For Dummies (+ Free Online Practice)

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Chapter 5

Polynomial functions have graphs that are smooth curves. They go from negative infinity to positive infinity in a nice, flowing fashion with no abrupt changes of direction. Pieces of polynomial functions are helpful when modeling physical situations, such as the height of a rocket shot in the air or the time a person takes to swim a lap depending on their age.

Most of the focus on polynomial functions is in determining when the function changes from negative values to positive values or vice versa. Also of interest is when the curve hits a relatively high point or relatively low point. Some good algebra techniques go a long way toward studying these characteristics of polynomial functions.

In this chapter, you’ll work with polynomial functions in the following ways:

Solving quadratic equations by factoring or using the quadratic formula

Rewriting quadratic equations by completing the square

Factoring polynomials by using grouping

Looking for rational roots of polynomials by using the rational root theorem

Counting real roots with Descartes’s rule of signs

Using synthetic division to quickly compute factors

Writing equations of polynomials given roots and other information

Graphing polynomials by using end-behavior and the factored form

Don’t let common mistakes trip you up; keep in mind that when working with polynomial functions, your challenges will include

Watching the order of operations when using the quadratic formula

Adding to both sides when completing the square

Remembering to insert zeros for missing terms when using synthetic division

Recognizing the effect of imaginary roots on the graph of a polynomial

251–260Find the solution set for the equation by factoring.

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261–265Use the quadratic formula to solve the equation.

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266–270Solve the equation by completing the square.

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271–276Find the real roots of the polynomial.