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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.

When you have to factor a trinomial where there is no common factor and the x^2 term is greater than 1, I call this "Advanced Trinomial Factoring." Before trying to understand this topic, be sure you understand regular trinomial factoring! If you need extra help, please see my video on Trinomial Factoring in Basic Algebra!

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

Grouping of terms to factor polynomials can be tricky. You probably never heard of "Junk Trinomials"! Neither did I, until this idea came to me as I was teaching one day!!

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!

This is an important section: Solving quadratic equations by factoring! Remember, you must set the equation equal to zero, then factor the resulting polynomial. If the resulting polynomial cannot be factored, then other methods called "Completing the Square" or "Quadratic Formula" (See Intermediate Algebra, Chapter 4) may be used.

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.

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.

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.

Complex fractions are fractions that contain fractions in the numerator and/or denominator of the fraction. Hopefully, this video from one of my Intermediate Algebra classes will help you understand how to simplify these fractions.

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.)

This video from 2003

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.

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 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!

Rob at Stickmarsh

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