- 5.3 Polynomials and Polynomials Functions (Week 7-Wednesday Classes)
- Explain what terms are and what polynomials are using examples. Do not emphasize on jargons like monomials, binomials, and so on so forth.
- Like Terms
- Evaluation $P(a)$ of a polynomial $P(x)$ at $x=a$
- Adding and subtracting polynomials by combining like terms
- Multiplying two polynomials by distributive property and simplify the product. Also discuss FOIL as a special case, multiplying two binomials.
- Special Products:
- Notion of Factoring as the reverse process of multiplying
- Finding the GCF (Greatest Common Factor) of polynomials
- Factoring polynomials by Grouping
- Factoring quadratic polynomials, i.e. trinomials of the form $ax^2+bx+c$. As an application, also go over examples like factoring $16x^2+24xy+9y^2$.
Please do not mention about factoring trinomials of the form $ax^2+bx+c$ by grouping. It is not really recommendable method for students.
- Factoring by Substitution
Introduce formulas of special products and show examples of factoring using those formulas.
- $a^2+2ab+b^2=(a+b)^2$, $a^2-2ab+b^2=(a-b)^2$
- $a^3+b^3=(a+b)(a^2-ab+b^2)$, $a^3-b^3=(a-b)(a^2+ab+b^2)$
- Zero-Factor Property
- Steps of Solving Polynomial Equations by Factoring (p. 317)
and go over as many examples as you can.
Please cover everything presented in the textbook. Students would understand better if you use analogy between rational numbers and rational expressions.