Chapter 7, Section 5.

The process steps for factoring are contained in a handout.  My website has a copy of this handout, see http://iweb.tntech.edu/ddbryant/dspm0850.htm

For the sum and difference of two cubes, here is an alternate pattern.  I teach all other factoring skills as given on the website.

Suppose you have 8a3 – 27b3. 
Think of 8a3 = (2a)3 , where "2a" is the first term = F
and
27b3 = (3b)3 , where "3b" is the last term = L.

 

Then the pattern is this:

  F3  –   L3   =  (F) 3– (L) 3 =  (F –  L) (  F2   +   FL  + L2)
8a3 – 27b3 =  (2a)3- (3b)3= (2a - 3b)(4a2 + 6ab+ 9b2 )

Likewise for  8a3 + 27b3, the pattern is this:

   F3  +   L3   =  (F) 3+ (L) 3 =  (F + L) (  F2   -   FL  + L2)
8a3 + 27b3 =  (2a)3+ (3b)3= (2a + 3b)(4a2 - 6ab + 9b2 )

Part of this lesson is to review solving quadratic equations.

To solve a quadratic equation by factoring, follow these process steps:
1.     Put the equation in standard form, that is ax2 +bx + c = 0 (0 on one side and decreasing powers of the variable on the other.
2.     Factor completely.
3.     Set each factor equal to 0 (see the zero-factor property, page 321).
4.     Solve each linear equation produced in step 3.
5.     Check each solution.

Note:  An equation of degree 2 generally has two solutions, degree 3 generally has three solutions, etc.

Before class you might want to go back to page 322 and review examples 1-4.  You will also want to look at the summary of factoring techniques in Chapter 5, section 5, page 317 as well as the new information in Chapter 7, section 5.  If you have additional time, feel free to also look at the summary of factoring techniques on this website.