4.5 Solving Polynomial Equations by Factoring

Lesson Plan 4.5: Solving Polynomial Equations by Factoring

Objectives:

• Learn the general approach to any factoring problem.
• Use the zero-factor property to solve equations.

Suggested Lecture Breaks:

• MWF: You have three days. Spend the first day exclusively on review and problem 1. The second day, get through the first part of the zero factor property lecture. The third, finish the material.
• MW/TR: You have two days. Spend the first day exclusively on review and problem 1. The second day, work on the zero factor property.

Suggested Lecture Notes:

General Approach to Factoring

• List the steps of a ``general approach" to a factoring problem, as in the Guide to Factoring in the workbook. This serves as a good review of everything we've learned on factoring thus far.

Zero Factor Property

Suggested Lecture part I: (15-20 minutes lecture)

• Ask students to give you the definition of the zero-factor property.
• Practice: Ask students to do #2. Afterward, take some time to talk about the subparts, especially parts (c) and (d).
• Provide examples with nonzero right hand side and requiring simplification before factoring, such as: (x-1)(x-2)=12 and m^2+2m-8=0. Do it as a whole class, let students tell you that you need to first get these into factored forms equal to 0.
• Practice: #3

Suggested Lecture part II: (10-15 minutes lecture)

• Do a word problem together as a class. Ask students what is given and what they need to solve, what formulas/ relationship they should use. Ask one student to set up the equations for you. Then give students several minutes to solve it. You should go around helping and giving hints if necessary. For example, you should remind students of substitutions and all the other techniques they learned before.
• Practice: #4-#8.

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. Also encourage them to write down what methods/formulas they had to use in each problem for when they review later.
• Length, time, etc. should be of positive values. Drop the negative answers in these situations.
• Question 1(r): This one is tricky and uses the difference of squares formula three times. It might be a good one to go over as a class.
• Question 7: This one may trip students up. First, encourage them to ignore the parts and write an equation representing the main sentence. For part (b), if necessary, ask the students what number they would use to represent ground height.