Question

Polynomial 1: 3x^4-2x^3+5x^2-7 Polynomial 2: x^3+4x^2-6x+2 Sum: (3x^4-2x^3+5x^2-7)+(x^3+4x^2-6x+2) Combine like terms 3x^4-x^3+9x^2-6x-5 Difference: (3x^4-2x^3+5x^2-7)-(x^3+4x^2-6x+2) Combine like terms 3x^4-3x^3+x^2+6x-9 Product: 3x^7+10x^6-21x^5+38x^4-41x^3-18x^2+42x-14 Quotient: 3x-14+(70x^2-90x+21)/(x^3+4x^2-6x+2)

1. Find either the sum, difference, product, or quotient of your classmates' 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?


1. Find either the sum, difference, product, or quotient of your classmates' 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?


1. Find either the sum, difference, product, or quotient of your classmates' 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?


1. Find either the sum, difference, product, or quotient of your classmates' 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 how you agree in your own words. Write in one paragraph start with I see what you mean

Answer 1

I see what you mean regarding the approach to polynomials and the methods of combining them. Focusing on one operation at a time, such as finding the sum or product, makes the problem more manageable and less overwhelming. By examining the leading and constant terms, we can establish rules to quickly identify the first and last terms of the resulting polynomial. For instance, the first term of a sum or product is typically determined by the leading terms of the individual polynomials, while the last term results from the constant terms. However, these rules can have limitations when polynomials contain more complicated structures, such as multiple variables or when higher-degree terms combine in unexpected ways, which can change the anticipated outcome.