I understand what you mean. It helps to focus on one operation at a time, like finding the sum or product, to make things easier to handle. By looking at the leading (first) and constant (last) terms, you can use some rules to quickly find these terms in the new polynomial. Generally, the first term comes from the leading terms of the polynomials we're adding or multiplying, while the last term comes from the constant terms. However, these rules can get tricky when polynomials have more than one variable or when higher-degree terms combine in unexpected ways, which can change what we expect to see.

Question

I understand what you mean. It helps to focus on one operation at a time, like finding the sum or product, to make things easier to handle. By looking at the leading (first) and constant (last) terms, you can use some rules to quickly find these terms in the new polynomial. Generally, the first term comes from the leading terms of the polynomials we're adding or multiplying, while the last term comes from the constant terms. However, these rules can get tricky when polynomials have more than one variable or when higher-degree terms combine in unexpected ways, which can change what we expect to see.
1. Find either the sum, difference, product, or quotient of the post above' polynomial expressions. Choose only one operation; you do not need to perform all four.

2. Create rules for how to approach finding the first and last terms of your peers' polynomial expressions, without working them out fully. Explain how you derived your rules. Do any of these rules have limitations?

write in your own words

write in one paragraph explain how your rules were derived.

start the paragraph with I see what you mean.

GPT-4o mini · Answer

I see what you mean. To determine the first and last terms of polynomial expressions, I developed a couple of straightforward rules based on the fundamental properties of polynomial addition and multiplication. For addition, the first term will be the leading term (the term with the highest degree) from the polynomial with the largest degree, while the last term is simply the sum of the constant terms from both polynomials. In multiplication, the first term arises from multiplying the leading terms of both polynomials, and the last term is the product of the constant terms. These rules are derived from the structure of polynomials: the leading term always takes precedence in determining the highest degree, and the constant terms only affect the ends of the polynomial. However, these rules can become complicated when dealing with polynomials that contain multiple variables or when there are several terms contributing to the leading or constant positions, as they may lead to unexpected combinations that aren't covered by the basic rules.