Chapter+06+Notes

Now that we have worked with linear functions and quadratic functions we are going to move on to higher order functions. This chapter explores their atributes and we finally have enough information to understand the Fundamental Theorem of Algebra.

In this first section we are introduced to polynomials and how people in the math world classify and name different functions and equations.

Now that we have an idea of how to name our functions we are learning how to use the graphing calculators to write equations for us from a set of data points. The instructions given here are for the TI-83 and TI-84. A reminder here that the manual for these calculators is provided in the links for Chapter 3 Notes.

In this second section we are beginning a look at the role that factors have for polynomial functions. To do this we first need to know how to factor and get our zeros.

Since we have worked on finind factors of polynomials we need to know what to do with them and that is what this section goes into including a quicker way to graph these functions.

We all remember (with a little regret) how to do long division. Now that we are finding factors of polynomials we are going to revisit this style of mathematics using the variables.

An easier way to perform division is a process called synthetic Division. This method only works, however, if the divisor is a linear term and has a lead coefficient of 1.

In this section we are beginning to solve polynomials. The first method discussed is graphing and two different approaches are shown here.

As we move up to higher degree polynomials can be factored following patterns thaat we learned before. These skills are now going to all be combined to find the solutions for x.

We now will begin to combine all of these ideas and use them together to solve polynomials. When we are working on solving these equations it always helps to have a list of numbers that are possibilities, and that is what the Rational Root Theorem provides for us.

We do not always have polynomials whose roots are rational numbers. In these cases the Irrational Root Theorrem and the Imaginary Root Theorem take effect. Basically, these roots always come in pairs.

To end our semester's study of math we finally arrive at the Fundamental Theorem of Algebra, the main idea that this type of math is based on. The ideas covered in this section were covered informally in others, but here we finally put it to exact words.