Vocabulary Unit 3

Polynomial Leading Coefficient Degree Term Factor Fundamental Theorem of Algebra Range

x-intercept y-intercept Increasing/Decreasing Intervals Relative Maximum(s) Absolute Maximum

Relative Minimum(s) Absolute Minimum End Behavior Zero Root Synthetic Division

Long Division Remainder Theorem Factor Theorem Complex Number Imaginary Number Multiplicity

After

We spent yesterday reviewing adding, subtracting, multiplying, and dividing polynomials. Below are some practice problems to help make sure we know what we are doing. After the practice are some videos to help you in case you need it.

Polynomial Practice:

We spent yesterday reviewing adding, subtracting, multiplying, and dividing polynomials. Below are some practice problems to help make sure we know what we are doing. After the practice are some videos to help you in case you need it.

Polynomial Practice:

This section looks at polynomials as a set of linear factors (x + a), and there zeros (solutions, roots, or x-intercepts). We will look at the factor theorem and the concept of multiplicity. Finally, we look at what relative minimums and maximums are and how to determine their value. This sections relates to Chapter 5-2 in our online or classroom Algebra 2 Textbook. Feel free to look there to help you understand this material.

In this next section, we move into solving "simple" polynomial equations by factoring or graphing (with a graphing calculator).

For the factoring part, we need to remember some other factoring techniques;

Greatest Common Factor

Quadratic Trinomials

Perfect Square Trinomials

Difference of Squares

Factoring By Grouping

Sum or Difference of Cubes

We have practiced these in class but if you need more review, go to youtube, teachertube, or Khan Academy for some helpful videos. Below are some practice problems.

We have added a couple skills, long division, synthetic division, and the remainder theorem. We are primarily concerned with being able to factor larger polynomials. Synthetic division helps in that task. Long division is used when synthetic division can't be used. We have also used synthetic to solve some simple volume problems. Below is practice for these ideas.

The last two new concepts for this section are the CONJUGATE ROOT THEOREM and the RATIONAL ROOT THEOREM. These are used to help us solve even more complicated polynomials. The actual theorems and examples will be (or have been) discussed in class. Below you will find some practice for these concepts.

Below you will find the study guide for unit 3. The answer key for this study guide will be posted as soon as it is finished.

Study guide answer key.