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Kansas State Polytechnic

0.1 Factoring

1: Introduction and Common Factor

This video covers:
*Factoring is the most important process that you will learn in College Algebra and subsequent classes
*Review of Polynomial Classification (naming polynomials), Addition/Subtraction/Multiplication of Polynomials
*The difference between dividing and factoring
*The 'Common Factor' technique, when you should look for it, and what it looks like
*How to check the common factor technique

Examples:
Common Factor Examples


2: Factor by Grouping

This video covers:
*The steps of 'Factor by Grouping' using the Common Factor technique
*How many terms emphasizes Factor by Grouping
*Why to use underlines rather than parenthesis to group the terms
*Why the parenthesis must match for Factor by Grouping to work
*How to check the Factor by Grouping technique
*Why your final format should have parenthesis around both sets of terms

Examples:
Factor by Grouping Examples

 


 3: Factor by Trinomial Introduction and Simple Examples

This video covers:
*Review of the FOILing process because it is the opposite than the factor by Trinomial technique
*Factor by Trinomial technique using the FOIL process backwards, including the proper signs
*How many terms emphasizes the Trinomail technique
*What order the set of parenthesis should be in
*How to check the factor by trinomial method

Examples:
Simple Trinomial Examples

 


 4: Factoring More Complicated Trinomials

This video covers:
*Reminder that polynomials should always be in descending order, especially before you try to factor them
*Reminder to always look for any common factors first
*Why trinomial factoring is more difficult when you have a number with the first term
*What numbers to start with in the guess and check method
*A helpful hint with trinomials and common factors
*A suggestion to not erase you trial and errors, so you don't keep trying the same combination
*Reminder of how to check your trinomial factoring
*Reminder of what descending order looks like with two variables
*When to condense the two factors as a binomial squared

Examples:
Difficult Trinomial Examples

 


 5: Factoring the Difference of Squares

This video covers:
*Review of all the other techniques so far (up until 3:15)
*How many terms emphasizes the Difference of Squares technique
*How the name, Difference of Squares, fully explains this technique - it must be the difference (subtraction)
*How this is a special case of the opposite of FOILing
*What the signs of Difference of Squares are guaranteed to be
*How to check the difference of square techniques
*Reminder to check that the polynomial is in descending order and to look for common factors first
*Just because you factored using one technique doesn't mean you have finished factoring - always look to factor farther!
*Review of the vocabulary word, conjugates
*The formula of difference of squares

Examples:
Difference of Square Examples

 


6: Factoring Out Negatives

This video covers:
*When it is best to factor out a negative
*Reminder to check that the polynomial is in descending order and to look for common factors first
*Reminder of just because you factored using one technique doesn't mean you have finished factoring - always look to factor farther!
*Reminder to always check factoring by multiplying it out

Examples:
Factoring out Negative Examples

 


7: Factoring Completely

This video covers:
*Review of all the factoring techniques
*The checklist that you should follow when factoring any polynomial - how all the techniques work together
*Reminder to check that the polynomial is in descending order and to look for common factors first
*Reminder of just because you factored using one technique doesn't mean you have finished factoring - always look to factor farther!
*Reminder to always check factoring by multiplying it out
*Reminder to copy all work from step to step so you don't lose any important details
*Reminder that factoring is your 'best friend', the most important technique for college algebra and any subsequent classes

Examples:
Factor Completely Examples

 


 8: Calculus Factoring Examples

This video covers:
*Review of common factor
*How to factor examples when there are multiple factors in common, including factors in parenthesis
*How to factor common factors with negative exponents
*Review of negative exponents

Examples:
Calculus Factoring Examples

 


 

Other factoring techniques not covered: Factoring the sum and difference of cubes
Examples covered:
Sum/Difference of Cube Examples