4.2 Algebra of Functions

Lesson Plan 4.2: Algebra of Functions

Objectives:

• Recognize polynomials, and be able to simplify the addition and/or subtraction of polynomials.
• Become comfortable with adding, subtracting, and multiplying polynomials.

Suggested Lecture Breaks:

• MWF: You have two days. Get through Problem 5 on the first day.
• MW/TR: You have 1.5 days. Get through Problem 6 on the first day.

Suggested Lecture Notes:

• Define polynomial; point out the numerical coefficient and degree of the term(s). Also point out the leading term and leading coefficient.
• Provide examples of polynomials, pointing out the coefficients and degrees. Also provide a few nonexamples.
• Provide examples of adding and subtracting polynomials (notice we are NOT emphasizing the notation used in the text for this, e.g. we have avoided using the notation $(f+g)(x)$).
• Similarly, provide examples of multiplying polynomials. Be sure to do a simple example such as:
  • $3x^2(5x^5)$
• Next, provide at least one example using the distributive law.
• Next, work on multiplying monomials. While the text provides many methods of approach, focus on teaching what is known as the FOIL method but teach it as the distributive rule (i.e. * Since students have to think about this as the distributive method for products of polynomials with more than 2 terms, when introducing foiling first introduce it as distribution: (2x + 2)(4x^2-1) = 2x(4x^2-1) + 2(4x^2-1)=8x^3-2x+8x^2-2, and then explain how foiling produces the same result.
• Avoid things like the box method. It is okay if students wish to use other methods in their work, however.

Comments on the handout:

• Problem 5: These are tricky for students. Encourage them to first write out the addition or subtraction, and THEN plug in the value to avoid mistakes.
• Problem 7g: Remind students what it means for the exponent to be outside the parentheses.