Basic Algebra Videos by Dr. Rapalje

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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!

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) !!

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.

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.

  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. 

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!

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.

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! 

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!