## Monday, January 29, 2007

### Next Lesson: Polynomials and the Number Line Model

Intersession is complete, and we're back to regular school (i.e. normal crazy instead of crazy crazy).

In the next Algebra 2 lesson, we will start with the basic understanding of what a polynomial is, and how to categorize them by degree and number of terms. Students also need to know how to write a polynomial in standard form and identify the leading coefficient. Nothing too exciting or creative here, just some definitions to get out of the way.

The second half of the class should be a little more interesting. Based on the work in the previous class, students should be able to look at a set of linear graphs and determine where the x-intercepts of the product function will be. From there, we will learn how to generate number line models. Students will plot the x-intercepts on the number line, and then write, in interval notation, the intervals that are defined. Students will look at the lines to determine the sign of the product function in each interval, putting a "+" above or a "-" below the number line in each interval. They will then sketch what a reasonable graph might look like based on this, and then check their work by graphing on the calculator.

After practicing this, we will move on to doing the same thing, but given a factored form polynomial function instead of the liner graphs.

If all goes well, we can move into working with functions that have repeated roots in the next class, along with solving factored form polynomial inequalities.