Lesson 2: Operations on Polynomials

What is the difference when adding polynomials compared to subtracting polynomials?
Does adding/subtracting polynomials effect the exponents?

A.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Lesson Description In this lesson, students learn that polynomials are combined following the same basic principles as real numbers, but with a strict focus on "like terms." Key skills include: Combining Like Terms: Identifying terms with the exact same variable and exponent (e.g., 3x^2 and 5x^2 can be added, but 3x^2 and 5x cannot).Addition of Polynomials: Using both horizontal and vertical formats to group and sum terms. Subtraction of Polynomials: Mastering the "Distributive Property of -1." Students learn that subtracting a polynomial is the same as adding its opposite, requiring them to change the signs of every term in the second polynomial. Standard Form Persistence: Ensuring that the final resulting expression is written in descending order of degree.
Purpose
The purpose of Section 13.2 is to develop procedural accuracy and attention to detail. Polynomial addition and subtraction are conceptually simple but high-risk for "sign errors." By mastering these operations, students build the foundational discipline required for the more complex multiplication and division coming in later sections. This section reinforces the idea that algebra is a system of rules that must be followed consistently to maintain the equivalence of expressions.
Depth of Knowledge (DOK) Level
DOK Level 1 & 2
Level 1 (Recall & Reproduction): Identifying like terms and performing basic addition/subtraction where sign changes are not required.
Level 2 (Skill/Concept): Applying the distributive property to a subtraction problem. Students must recognize that the minus sign applies to the entire parentheses and successfully navigate the "change the sign" process across multiple terms. It requires a coordinated sequence of steps to reach a simplified final form.

have students perform the operations on a variety of polynomials

"you try" on page 304