Sept. 21 Class

Learning Goals: Understand common factoring.

Today I discussed how factoring is the opposite of expanding.

For now it might seem arbitrary, but in the coming weeks we will find that factoring will help us solve some tricky problems.

The first kind of factoring is called Common Factoring.  We do this by finding out what is a common factor among all the terms in an expression.  In other words, what can we divide every term by?

Example: Factor .

Solution: All the terms cal be divided by 2, so we can put a 2 out front and divide every term by 2.

We have to check if there are anything else that all the terms can divide by.  In this case we see that there is x in every term.  So we can go ahead and factor the x as well.

We could have factored the 2x in one step as well.  The key to know when to stop is to make sure there is nothing else you can divide all the terms by.

Here are a few more complicated examples.

Example: Factor .

Solution: There is a common factor of 30xy.

Example: Factor .

Solution: The common factor is (3x+1).  In the first term, if we divide (3x+1) by (3x+1) we are left with 1.  In the second term we are left with -2x.  Here is what the solution will look like:

Homework: P. 92 #2, 3cd, 5cd, 6def, 7-14