339. The average amount of time (in seconds) it takes a person to complete an obstacle course depends on the person’s age. If the function
340. The average amount of time (in seconds) it takes a person to complete an obstacle course depends on the person’s age. If the function
Chapter 7
Polynomial Functions and Equations
A polynomial function is one in which the coefficients are all real numbers and the exponents on the variables are all whole numbers. A polynomial whose greatest power is 2 is called a quadratic polynomial; if the highest power is 3, then it’s called a cubic polynomial. A highest power of 4 earns the name quartic (not to be confused with quadratic), and a highest power of 5 is called quintic. There are more names for higher powers, but the usual practice is just to refer to the power rather than to try to come up with the Latin or Greek prefix.
The Problems You’ll Work On
In this chapter, you’ll work with polynomial functions and equations in the following ways:
Determining the x and y intercepts from the function rule (equation)
Solving polynomial equations using grouping
Applying the rational root theorem to find roots
Using Descartes’ rule of sign to count possible real roots
Making use of synthetic division
Graphing polynomial functions
What to Watch Out For
Don’t let common mistakes trip you up; watch for the following ones when working with polynomial functions and equations:
Forgetting to change the signs in the factored form when identifying x-intercepts
Making errors when simplifying the terms in f(–x) applying Descartes’ rule of sign
Not changing the sign of the divisor when using synthetic division
Not distinguishing between curves that cross from those that just touch the x-axis at an intercept
Graphing the incorrect end-behavior on the right and left of the graphs
Recognizing the Intercepts of Polynomials
341–350 Find the intercepts of the polynomial.
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Factoring by Grouping to Solve for Intercepts
351–360 Find the intercepts of the polynomial. To find the x-intercepts, use factoring by grouping.
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Applying the Rational Root Theorem to Find Roots
361–370 Use the Rational Root Theorem and Descartes’ Rule of Signs to list the possible rational roots of the polynomial.
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