COLLEGE ALGEBRA
MATH 110
Southwestern   
Adventist University 
 
   Distance Education Lawrence E. Turner, Jr., Ph.D.  


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Basic Algebraic Operations


Barnett, Ziegler, and Byleen, chapter 1


Winners never quit,
Quitters never win.


sections:

   1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 1-7

Much of this chapter should be a review of elementary algebra concepts. The primary concern is about properties of real numbers and basic manipulation of algebraic expressions.

objectives:
  • describe the sets of natural numbers, integers, rationals, and reals
  • classify a value in terms of a standard number set
  • explain what is meant by closure
  • tell which set of numbers is closed under the common arithmetic operations
  • determine the decimal representation of a number
  • describe the difference in the decimal representation of a rational and an irrational number
  • explain and give examples of what the commutative and associative properties are
  • tell which of the common arithmetic operations are commutative and associative
  • tell what is meant by an identity element for a given operation
  • explain what is meant by the distributive property
  • perform arithmetic operations on rational numbers (fractions)
  • use a natural number exponent
  • define what is meant by a polynomial
  • combine like terms to simplify a polynomial expression
  • simplify expressions involving numbers using the standard order of evaluation
  • add and subtract polynomials
  • multiply polynomials
  • define a prime number
  • determine if a given number is prime
  • factor a number into prime factors
  • find the greatest common factor of two numbers
  • factor a polynomial expression
  • use special factoring formulas for difference of squares, etc.
  • reduce rational expressions
  • combine rational expressions
  • rationalize a denominator
  • simplify compound fractions
  • use integer exponents
  • simplify expressions involving arithmetic operations with exponents
  • use the properties of exponents
  • combine numerical values using scientific notation
  • define an n-th root
  • use rational exponents
  • convert from radical to exponent notation and vice versa
  • use the properties of radicals to simplify expressions
  • compute a square root of a positive number
  • use the laws of square roots to simplify expressions involving radicals
  • use properties of exponents to simplify expressions
 
© 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 by Lawrence Turner