 5.3 Polynomials and Polynomials Functions (Week 7Wednesday 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
 5.4 Multiplying Polynomials (Week 7Wednesday Classes, Thursday classes, Friday Classes)
 Multiplying two polynomials by distributive property and simplify the product. Also discuss FOIL as a special case, multiplying two binomials.
 Special Products:
\begin{align*}
(a+b)^2&=a^2+2ab+b^2\\
(ab)^2&=a^22ab+b^2\\
(a+b)(ab)&=a^2b^2
\end{align*}  5.5 The Greatest Common Factor and Factoring By Grouping (Week 7Thursday Classes, Friday Classes, Week 8Wednesday Classes)
 Notion of Factoring as the reverse process of multiplying
 Finding the GCF (Greatest Common Factor) of polynomials
 Factoring polynomials by Grouping
 5.6 Factoring Trinomials (Week 7Thursday Classes, Friday Classes, Week 8Wednesday classes)
 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
 5.7 Factoring by Special Products (Week 9Wednesday/Thursday/Friday Classes)
 $a^2+2ab+b^2=(a+b)^2$, $a^22ab+b^2=(ab)^2$
 $a^2b^2=(a+b)(ab)$
 $a^3+b^3=(a+b)(a^2ab+b^2)$, $a^3b^3=(ab)(a^2+ab+b^2)$
 5.8 Solving Equations by Factoring and Problem Solving (Week 9Monday/Wednesday/Friday classes)
 ZeroFactor Property
 Steps of Solving Polynomial Equations by Factoring (p. 317)
 6.1 Rational Expressions, 6.2 Adding and Subtracting Rational Expressions (Week 10Monday/Wednesday/Friday classes)
Introduce formulas of special products and show examples of factoring using those formulas.

Discuss
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.