Basic Algebra Videos by Dr. Rapalje

Section 2.02 Factoring Numbers

Do you have “Math Anxiety”? This video “Basic Algebra: Factoring” was my first, and I was VERY nervous! After a couple of minutes of taping, I knew I wasn't doing very well, so I stopped the video, went outside, and took a couple of laps around the building with an anxiety visit to the restroom. I went back to the classroom, knowing that to do this video, I needed to teach to the STUDENTS, and NOT to the CAMERA! So when I focused on the students, we did the entire 90 minute video in ONE take!

Section 2.03 Factoring the Common Factor

The first step in ANY factoring problem is to factor out the common factor. In a later section, I will introduce something I call the "Factoring Two Step." For now, enjoy these "one step" problems. Just remember, when you are taking out the common factors, be sure to get ALL the common factors.

Section 2.04 Factoring Trinomials

In order to factor a trinomial, you must first understand how to take the product of two binomials. I use a method called "F OI L." (FIRST, OUTER, INNER, LAST)

To factor a trinomial, I reverse the steps of "F OI L" and write "F L OI." You probably haven't heard this method called "F L OI" because I made it up myself, right here in FL (orida) !!

Section 2.04 Factoring Two Step

Perhaps you never heard of the "Factoring Two Step." That's probably because I made it up myself! The first step in ANY factoring problem is to take out the COMMON FACTOR! Make sure when you do this step that you get ALL the common factors! Then, in the second step, look to see if there is a TRINOMIAL that can be factored. Sometimes there is a factorable trinomial, sometimes not! Be sure to factor completely!!

Sec 2.05 Difference of Squares, Perfect Square Trinomials

Do you know your "Perfect Squares"? 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and 169. Do you recognize these special numbers as the squares of the first counting numbers??? If you know these numbers, then you will think this is a VERY easy section! Then fasten your seat belt when we get to the exercises that I call "Advanced Trinomial Factoring!" The following section from Intermediate Algebra on this topic may be helpful.

Section 2.06 Advanced Trinomial Factoring

What I call "Advanced Trinomial Factoring" is factoring trinomials where the coefficient of x^2 is other than 1. In the Basic Algebra factoring video, I ran out of time, with very little time to explain "Advanced Trinomial Factoring." Perhaps this video from an Intermediate Algebra class (Intermediate Algebra Section 2.01) will help!

Section 2.09 Solving Quadratic Equations by Factoring

What good is all this factoring?? For one thing, factoring allows you to solve certain quadratic equations (that is, equations that involve an x^2 term!). Of course, as you continue in higher mathematics, factoring has many other applications as well. This video from my Intermediate Algebra, Section 2.02, may be helpful.

Section 3.01 Reducing Fractions

Before you begin to work with algebraic fractions, in particular reducing fractions, make sure you are GOOD at factoring! Remember to NEVER divide out TERMS in reducing fractions! You can ONLY divide out FACTORS! This is why the FIRST step in reducing fractions is to FACTOR completely!! This video is from an Intermediate Algebra class in about 1993.

Section 3.02 Multiplying and Dividing Fractions

Before you multiply or divide algebraic fractions, make sure you are GOOD at factoring! Remember to NEVER divide out TERMS in reducing fractions! You can ONLY divide out FACTORS! This is why the FIRST step in multiplying or dividing fractions is to FACTOR completely!! This video is from an Intermediate Algebra class in about 1993.

Section 3.04 Adding and Subtracting Fractions

When you add or subtract fractions, the first step is ALWAYS to find a COMMON DENOMINATOR. Usually (but not always!) the best common denominator is the LEAST COMMON DENOMINATOR (LCD). In order to find the LCD, it is helpful to FACTOR all the denominators. Again, FACTORING is a critical prerequisite skill for this topic. This video is from an Intermediate Algebra class in about 1993.

Section 4.01 Graphing a Line by Plotting Points

One method of graphing a line or a curve of any kind is to plot a few points in an x,y table. How many points you need to plot depends upon how complicated the curve is and also how clever you are in finding the right points to graph!

Section 4.02 Graphing by Slope-Intercept Method

When the equation of a straight line is given in the form y=mx+b, this is the EASIEST way to graph it!

Section 4.02 Converting to Slope-Intercept Form

When the equation of the line is NOT in slope-intercept form, perhaps when it is in standard form like Ax+By=C, you may want to convert the equation to slope-intercept form by solving for y.

Section 4.03 Graphing a Line by Two Intercept Method

If the equation of a line is in Standard Form Ax+By=C, then the easiest way to graph the line is by the Two-Intercept Method. If C=0, then there is only one intercept, so you will need to graph one additional point, or find the slope of the line. This video is coming soon!

Section 5.01 Simplifying Radicals (Square Roots)

Before you attempt this "radical" section, you need to know and recognize the first few PERFECT SQUARES: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and 169!

Section 5.02 Simplifying Cube Roots and Higher Radicals

In this section, you need to know and recognize the first few perfect cubes: 2^3=8, 3^3=27, 4^3=64, and 5^3=125!! For 4th powers, only two are small enough to be commonly used: 2^4=16 and 3^4=81. For 5th powers, only 2^5=32 is necessary to recognize.

Section 5.03 Adding and Subtracting Square Roots

In simplifying algebraic expressions, always combine LIKE terms. When terms involve radical expressions (square roots), always combine LIKE radicals. Never combine two radicals (square roots) unless they are LIKE radicals!

Section 5.04 Products of Square Roots

Congratulations on reaching my last video from Basic Algebra! If you liked these videos, try the next level: Intermediate Algebra!!

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