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Elementary Algebra

6. Polynomials and the Laws of Exponents

 

Description

 

    Since Algebra is the generalization of arithmetic, we explore arithmetic operations with variables.  In this topic, we explore the Laws of Exponents and Scientific Notation; classifying, adding, subtracting, multiplying and dividing polynomials and applications of polynomials to real world scenarios.

 

Sections of this topic include:

 

1.   Multiplication and Division with Exponents

 

     We begin how to simplify polynomials by first exploring the laws of exponents.  This group includes identifying bases and exponents; writing expressions using exponents; simplifying numeric expressions using laws of exponents; simnplifying numeric and algebraic expressions using laws of exponents; simplifying alebraic expressions using laws of exponents; simplify algebraic expressions using laws of exponents then evaluating with a given number.

 

2.   More on Exponents; Scientific Notation

 

    Building on our knowledge of laws of exponents; we explore more laws of exponents and scientific notation.  This group include simplifying numeric expressions using laws of exponents; simplifying algebraic expressions using laws of exponents; simplifying algebraic expressions using laws of exponents then evaluating with a given number; writing numbers in sicentific notation; writing numbers in decimal notation; writing numbers in scientific notation then simplifying; writing scienfici ntoation numbers from statements; writing numbers in decimal notation from statements.

 

3.   Adding and Subtracting Polynomials

 

     With a foundation now, we can explore polynomials including how to classify polynomials, and adding and subtracting polynomials.  Groups in this section include classifying polynomials; determining if expressions are polynomials; simplifying polynomials; adding poolynomials in a vertical format; subtracting polynomials in a vertical format; and adding and subtracting polynomials in a horizontal format.

 

4.   Multiplying Polynomials

 

     From adding and subtracting polynomails, we next explore how to multiply polynomails.  Groups in this section include multiplying a monomial by a polynomial; finding products and combining like terms; and finding products using the Foil method.

 

5.   Dividing Polynomials

 

     The last operation to master is to divide polynomials.  This group contains dividing expressions by a single term; solving division problems; polynomial long division; and solving applied problems using polynomial long division.

 

6.   More Applications

  

     This section includes applications of how polynomials and operations with polynomials can be used in the real world.

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