Question
MY polynomials 2x^3-4X^2+5X-1 (Degree 3) x^2-3x+2 (Degree 2) 1. SUM - (2x^3-4X^2+5X-1)+( x^2-3x+2) find like terms and combine final answer = 2x^3-3x^2+2x+1 2. DIFFERENCE - (2x^3-4X^2+5X-1)-( x^2-3x+2) distribute the negative (2x^3-4X^2+5X-1)+( -x^2+3x-2) now combine which = 2x^3-5x^2+8x-3 3.PRODUCT - (2x^3-4X^2+5X-1)x( x^2-3x+2) I used the box method to multiply my polynomials and combine like terms which = 2x^5-10x^4+21x^3-24x^2+13x-2 4. QUOTIENT- Using long divison to divide my polynomials the answer comes out to be 7x-5/x^2-3x+2
Find either the sum of the post above's polynomial expressions.
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 in one paragraph. start the paragraph with You've hit the nail on the head.
explain how you derived the rule
Find either the sum of the post above's polynomial expressions.
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 in one paragraph. start the paragraph with You've hit the nail on the head.
explain how you derived the rule
Answers
GPT-4o mini
You've hit the nail on the head when identifying the sum, difference, product, and quotient of polynomial expressions through systematic approaches. To find the first term of a polynomial expression, observe that it is derived from the highest degree term of each polynomial; for instance, in the product of two polynomials, multiply the leading coefficient of each. The last term, usually the constant, is achieved by identifying the constant term in each polynomial and combining them according to the operation being performed (like addition or multiplication). I derived these rules by recognizing patterns in polynomial manipulations, focusing on degree and coefficients. One limitation of these rules is that they may not easily extend to more complex operations or higher-dimensional polynomials without careful adjustment to keep track of all contributing terms.