Exponential Functions
Linera Equations
Simple Trinomials as Products of Binomials
Laws of Exponents and Dividing Monomials
Solving Equations
Multiplying Polynomials
Multiplying and Dividing Rational Expressions
Solving Systems of Linear Inequalities
Mixed-Number Notation
Linear Equations and Inequalities in One Variable
The Quadratic Formula
Fractions and Decimals
Graphing Logarithmic Functions
Multiplication by 111
Solving Systems of Equations - Two Lines
Solving Nonlinear Equations by Factoring
Solving Linear Systems of Equations by Elimination
Rationalizing the Denominator
Simplifying Complex Fractions
Factoring Trinomials
Linear Relations and Functions
Axis of Symmetry and Vertices
Equations Quadratic in Form
The Appearance of a Polynomial Equation
Subtracting Reverses
Non-Linear Equations
Exponents and Order of Operations
Factoring Trinomials by Grouping
Factoring Trinomials of the Type ax 2 + bx + c
The Distance Formula
Invariants Under Rotation
Multiplying and Dividing Monomials
Solving a System of Three Linear Equations by Elimination
Multiplication by 25
Powers of i
Solving Quadratic and Polynomial Equations
Slope-intercept Form for the Equation of a Line
Equations of Lines
Square Roots
Integral Exponents
Product Rule for Radicals
Solving Compound Linear Inequalities
Axis of Symmetry and Vertices
Multiplying Rational Expressions
Reducing Rational Expressions
Properties of Negative Exponents
Numbers, Factors, and Reducing Fractions to Lowest Terms
Solving Quadratic Equations
Factoring Completely General Quadratic Trinomials
Solving a Formula for a Given Variable
Factoring Polynomials
Decimal Numbers and Fractions
Multiplication Properties of Exponents
Multiplying Fractions
Multiplication by 50

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1. Prime Number: A prime number is any whole number greater than 1 that has exactly two divisors- itself and 1. (A number is a divisor of another number if it divides that number without a remainder.)

Ex: List the prime numbers that are smaller than 20.

1, 3, 5, 7, 11, 13, 17, 19

2. Writing the prime factorization of a number: To write the prime factorization of a number, write the number as a product of prime numbers.

Ex: Which of the following represents a prime factorization?

a. 12 = 6•2

b. 12 = 22 •3

b represents a prime factorization of 12.

You can use a factor tree to find a prime factorization. Express the given number as the product of two numbers. Then express each of those as the product of two numbers. Continue this process until the numbers no longer factor--you will then have the prime factors.

Note: The following divisibility tests will help you in deciding what numbers are factors of the given number.

Divisibility test for 2: A given number is divisible by 2 if it ends in an even digit.

Divisibility test for 3: A given number is divisible by 3 if the sum of the digits in the number is divisible by 3.

Divisibility test for 5: A given number is divisible by 5 if the last digit is 5 or 0.


3. Reducing a fraction to lowest terms: A fraction is said to be in lowest terms if the numerator and denominator have no common factors other than 1. To reduce a fraction to lowest terms, divide the numerator and the denominator by all of the factors that they have in common. If you do not know the common factors, write the prime factorization of the numerator and denominator, then divide out the common factors.