Algebra Tutorials!  
Monday 15th of July
Rotating a Parabola
Multiplying Fractions
Finding Factors
Miscellaneous Equations
Mixed Numbers and Improper Fractions
Systems of Equations in Two Variables
Literal Numbers
Adding and Subtracting Polynomials
Subtracting Integers
Simplifying Complex Fractions
Decimals and Fractions
Multiplying Integers
Logarithmic Functions
Multiplying Monomials
The Square of a Binomial
Factoring Trinomials
The Pythagorean Theorem
Solving Radical Equations in One Variable
Multiplying Binomials Using the FOIL Method
Imaginary Numbers
Solving Quadratic Equations Using the Quadratic Formula
Solving Quadratic Equations
Order of Operations
Dividing Complex Numbers
The Appearance of a Polynomial Equation
Standard Form of a Line
Positive Integral Divisors
Dividing Fractions
Solving Linear Systems of Equations by Elimination
Multiplying and Dividing Square Roots
Functions and Graphs
Dividing Polynomials
Solving Rational Equations
Use of Parentheses or Brackets (The Distributive Law)
Multiplying and Dividing by Monomials
Solving Quadratic Equations by Graphing
Multiplying Decimals
Use of Parentheses or Brackets (The Distributive Law)
Simplifying Complex Fractions 1
Adding Fractions
Simplifying Complex Fractions
Solutions to Linear Equations in Two Variables
Quadratic Expressions Completing Squares
Dividing Radical Expressions
Rise and Run
Graphing Exponential Functions
Multiplying by a Monomial
The Cartesian Coordinate System
Writing the Terms of a Polynomial in Descending Order
Quadratic Expressions
Solving Inequalities
Solving Rational Inequalities with a Sign Graph
Solving Linear Equations
Solving an Equation with Two Radical Terms
Simplifying Rational Expressions
Intercepts of a Line
Completing the Square
Order of Operations
Factoring Trinomials
Solving Linear Equations
Solving Multi-Step Inequalities
Solving Quadratic Equations Graphically and Algebraically
Collecting Like Terms
Solving Equations with Radicals and Exponents
Percent of Change
Powers of ten (Scientific Notation)
Comparing Integers on a Number Line
Solving Systems of Equations Using Substitution
Factoring Out the Greatest Common Factor
Families of Functions
Monomial Factors
Multiplying and Dividing Complex Numbers
Properties of Exponents
Multiplying Square Roots
Adding or Subtracting Rational Expressions with Different Denominators
Expressions with Variables as Exponents
The Quadratic Formula
Writing a Quadratic with Given Solutions
Simplifying Square Roots
Adding and Subtracting Square Roots
Adding and Subtracting Rational Expressions
Combining Like Radical Terms
Solving Systems of Equations Using Substitution
Dividing Polynomials
Graphing Functions
Product of a Sum and a Difference
Solving First Degree Inequalities
Solving Equations with Radicals and Exponents
Roots and Powers
Multiplying Numbers
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The 7 Forms of Factoring

A. Introduction:

Factoring is perhaps the most important skill you will need for much of Beginning Algebra, Intermediate Algebra, and even College Algebra and Finite Math. Let's look briefly at what it means to factor.

B. The Meaning of "to factor."

"To factor" means, "to rewrite as a product (things being multiplied)."

For instance, if we were to rewrite 12 as 9 + 3, we would be rewriting it as a SUM (things being added, or as terms).

However, if we choose to rewrite 12 as 3 * 4, we would be rewriting it as a PRODUCT (things being multiplied).

Then, we could make the following observations:

1. We factored the 12 as 3 * 4.

2. And, 3 and 4 are factors of 12.

C. Why Do We Factor?

There are a number of reasons why we factor but perhaps the two most important are:

1. We factor in order to simplify or reduce algebraic expressions so they are simpler and easier to work with.

2. We also factor in order that we may rewrite an equation so it fits the ZEROFACTOR PROPERTY. The Zero- Factor Property, very simply put, says that if the product of two "things" is zero, then one or both of the "things" must be zero. This allows us to set each of the "things" equal to zero and to solve equations we were not able to previously solve.

D. How to Master Factoring

As a warning, if you don't master it quickly, you will fall behind in understanding and applying new skills and concepts since so many of them will involve factoring. I suggest the following approach:

1. Memorize the names of the 7 Forms of Factoring given on the next page.

2. Notice how the name of each describes the structure or appearance of the next factoring form.

3. Think of each of the 7 Factoring Forms as a separate "room" in the larger "house" of Factoring.

4. In order to factor, we us a different procedure in each room. When you know which room you're in, then you can know what to do. This approach of giving attention to the names and accompanying structures is critical for success in your long- range math goals of completing the core requirement.

E. The 7 Forms of Factoring

Always 1. Greatest Common Factor (G. C. F.)

2. Difference of Two Squares

2 Terms 3. Difference of Two Cubes

4. Sum of Two Cubes

3 Terms 5. Perfect Square Trinomial

6. A Quadratic Trinomial

4 Terms 7. Factor by Grouping


Note: As you factor, you will be following a certain pattern: Always check for the Greatest Common Factor, and do that first. Then, look at what remains.

  • Is it Two Terms? Then look to see if it fits the structure of #2, #3, or #4 above.
  • Is it Three Terms? See if it fits the structure of #5 or #6.
  • Is it Four Terms? Then it may be #7, Factor by Grouping.
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