4.3 Factoring Polynomials

Lesson Plan 4.3: Factoring Polynomials

Objectives:

• Factor out the greatest common factor.
• Factor by grouping.
• Factor the difference of two squares.

Suggested Lecture Breaks:

• MWF: You have two days. The first day, get through problem 4.
• MW/TR: You have 1.5 days. The first (half) day, get through problem 3.

Suggested Lecture Notes:

• Discuss as a class what the GCF is.
• Provide examples of factoring out the GCF or binomial factor, such as:
  • $3x^5 - 27x^3 + 18 x^2$
  • $(x-16)(z+y) + (z-y)(x-16)$
• Provide at least one example of factoring out a negative common factor.
• Define the difference of squares formula.
• Provide at least two examples of using the difference of squares formula and one non-example. 10(c) on the reading guide makes an excellent non-example/discussion point.
• Discuss factoring by grouping (have students tell you what it is from RG).
• Provide examples of factoring by grouping:
  • $5x-3z+ax-bz$
  • $5x-bz-5z+bx$ %the other one doesn't factor by grouping (or at all)
• Finally, provide at least one example in which we can factor out a GCF before factoring by grouping:
  • $4a^3c-4a^2b^2c+8abc-8b^3c$

Comments on the handout:

• Encourage students to be thorough in the work and go one step at a time so that they may pay attention to plus and minus signs and the like.
• Problem 4(c): This can be factored more than once. Problems like this will show up on their WebWork assignments, so it's a good idea to go over it with them.