I see what you mean. To determine the first and last terms of polynomial expressions efficiently, I created a set of simple rules: for the first term, we look for the leading term of each polynomial, which is typically the term with the highest degree and the largest coefficient. By adding or multiplying these leading terms, we can easily identify the new first term. For the last term, we focus on the constant terms of each polynomial, as they provide the new constant in the resulting expression. These rules stem from the fundamental nature of polynomials, where the degree of the polynomial dictates the structure, and the constants provide the anchor points. However, these rules have limitations when dealing with polynomials that include multiple variables or when interactions between terms lead to unexpected behaviors, such as cancellation or the emergence of new terms that were not present in the original expressions.
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.
Find the sum of the post above's polynomial expressions.
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.
1 answer