Check out this great video from Intermediate Algebra!  Factoring the Common Factor and factoring Trinomials.  See also the videos on these topics on the Basic Algebra video page.

To factor polynomials larger than trinomials, you may need to try to "group" terms together and look for "patterns" that become apparent!

When factoring, always be looking for perfect squares and perfect cubes.  When you have a DIFFERENCE or SUM of CUBES, factoring can be performed using well-known formulas.  However, remember, you can't factor the SUM of SQUARES by ordinary methods you have learned so far! 

 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.

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.  

Solving fractional equations may look intimidating, but they are usually not nearly as bad as they look.  The first step is to find the common denominator for all the denominators, which may require factoring skills.  The trick is to multiply both sides of the equation by the LCD, which eliminates ALL the denominators.  However, after solving the resulting equation, you must make sure you didn't make any denominators ZERO, which is not allowed.   Such answers must be rejected.  (Circa 1993.)

A ratio and proportion problem is simply a fraction (with variables) equal to another fraction.  There are many excellent applications to everyday life.  The equations are usually very easy to set up and usually not difficult to solve, since the fractions can be eliminated in one simple step!  This is a good place to build your confidence.  The video is circa 2003.

 Literal equations tend to be intimidating, since the equations involve "letters" in the form of constants and variables.  Get past the intimidation, and they aren't really so bad after all.  This video, from 2003, includes my own "FSU" problem, solved in LIVING COLOR, i.e. GARNET and GOLD!  Strangely enough, like my own career, some "UF" colors  (blue and orange) might be involved!