Intermediate Algebra Chapter 5 Exponents, Polynomials, and Polynomial Functions Summary

Exponential Expressions: Definitions

Exponents may be any real number. The following formulas show how to manipulate exponential expressions regardless of the type of number in the exponent. These formulas also actually give meaning to negative and fractional exponents. No attempt will be made to give meaning to an irrational exponent. The same rules (formulas) for manipulating exponentials with natural number exponents apply to exponentials with irrational exponents

. formulas

formulas

Changing from scientific notation to standard notation:

A number in scientific notation like xxx.xxx X 10n can be changed to standard notation simply by moving the decimal point in xxx.xxx n places and omitting the power of 10. If n is positive the decimal is moved to the right and if n is negative the decimal is moved to the left.

Changing from standard notation to scientific notation:

A number in standard notation like xxx.xxx can be changed to scientific notation simply by moving the decimal point in xxx.xxx so that there is one significant digit to the left of the decimal. Count how many places the decimal was moved. If the decimal was moved n places to the right, multiply by 10^-n. If the decimal was moved n places to the left, multiply by 10n.

Polynomial: Terms: Introduction

Polynomial: Introduction

Polynomial: Arithmetic

Polynomial: GCF of Terms

When used as a noun the word factor refers to the individual parts of a product. When used as a verb (to factor) it means to write something as a product.

In many situations recognizing the number 136 as the product of 8 and 17 is a benefit. In such situations it is customary to claim that to factor 136 as (8)(17) is a simplification. In the same way factorizations of polynomials is usually a simplification. There are several methods for factoring polynomials. No single one of these methods is sufficient for all occasions, but in combination they can yield a factored (simplified) form of seemingly complex polynomials.

The very first step when factoring any polynomial is to identify the GCF of the terms of the polynomial and to write the polynomial as a product with the GCF as one of the factors. The Distributive Property is used to verify that the factorization is correct. A common phrase used to refer to this procedure is "to factor out the GCF".

Polynomial: Trinomial: Factoring: Easy

Polynomial: Trinomial: Factoring: Hard

Polynomial: Trinomial: Factoring: Special Products

Equations: Solving Equations in One Variable by Factoring

DrDelMath

Intermediate Algebra 4th Edition

by

K. Elayn Martin-Gay

Chapter Summary

Changing from scientific notation to standard notation:

Changing from standard notation to scientific notation: