Advanced Algebra 4.2 | Mr. Bartos Website

Overview:

This section focuses primarily on the roots or zeros of polynomials, and, in the process, on division of polynomials by binomials. We begin by dividing a polynomial by a binomial using long division. This is the same long division learned in grade school, but with a variable in the divisor instead of a constant. Since long division can be time-consuming, mathematicians have developed an easier way to divide a polynomial by a binomial. This method is called synthetic division. Students will be introduced to a shortcut for finding the remainder when a polynomial is divided by a binomial using the Remainder Theorem. Following the Remainder Theorem, is The Factor Theorem, which provides an easy way for determining whether a given binomial is a factor of a given polynomial. A specific use of synthetic division is to find the roots of a polynomial function. This section explains how to find all the rational roots of a polynomial function, using the Rational Zeros Theorem. The final section in this chapter deals with the complex roots of an equation, and introduces two new theorems. These are the Conjugate Zeros Theorem and the Fundamental Theorem of Algebra.

Day 67:

Notes: Dividing Polynomials using Long & Synthetic Division

Homework: Dividing Polynomials using Long & Synthetic Division

Day 68:

Notes: The Remainder and Factor Theorem

Homework: The Remainder Theorem

The Factor Theorem

Homework Solutions: The Remainder Theorem Key

The Factor Theorem Key

Day 69:

Notes: Solving Polynomial Equations Discovery Lesson

Teacher Key