You've hit the nail on the head with your calculations and approach to polynomial operations. To find the sum of the polynomials, you simply align like terms—terms with the same degree—and combine their coefficients. For the first term, look for the term with the highest degree, which is the leading term; in this case, it's \(2x^3\). For the last term, or the constant term, identify the standalone number without a variable; here, it’s \(-1\) from the first polynomial combined with \(2\) from the second. The rules I've derived for identifying these terms are straightforward: always start with the highest degree term to find the first term, and look for constant values for the last term. The limitation of these rules arises when polynomials are not presented in descending or ascending order, as you might miss intermediate terms. It’s important to check the overall structure before applying these rules to ensure accuracy.
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.
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