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Polynomials

Introduction and Summary

Table of Contents

Terms

This chapter explores polynomials, expressions which are the sum or difference of several individual monomial terms.

The first section explains how to classify polynomials. Polynomials are classified according to number of terms and degree.

The second section explores addition and subtraction of polynomials. To add and subtract polynomials, it is necessary to combine like terms.

In addition to adding and subtracting polynomials, we can also multiply polynomials. This is the topic of section three. The section begins with two specific cases -- multiplication of a polynomial by a monomial and multiplication of two binomials -- and ends with a general schema for multiplying any two polynomials.

The next section explores two special cases of binomial multiplication. The first case is multiplying a binomial by itself, or squaring the binomial. The result is a perfect square trinomial. The second case is multiplying of a sum of two terms by the difference of the same two terms. The result is a difference of squares.

The final two sections deal with factoring. Section five explains how to factor out a monomial, and section six explains how to factor trinomials of the form x 2 + bx + c into two binomials (x + d )(x + e) .

Polynomials equations are quite common in algebra and much of higher mathematics. Thus, it is important to know how to perform basic operations with them.

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