Comment by 🗡️ The_Jackal
Re: "I have another math question, and it's if this introduction…"
@darkghost Thank you. I do have a book on the GED and found a website for getting ready for the GED, but I'm so far behind in math I really should catch up with something like Khan Academy and take notes like I'm doing beforehand. Speaking of calculus, it's like how I'd always use a calculator for something like 343 times 567. I'll use a calculator, but I still want to understand the concept behind it and probably be able to do it with enough time if I did it on paper/didn't have a calculator or program for it. I'd also like to try keeping a notebook for myself that goes as indepth as I can in a way I can understand for myself, and then probably use other notebooks to have notes that might simplify them out for me, but that's for much later. I only have the one book for now, but it's messy and will definitely need redoing in anotner book later. My main worries when I write a note like I did in this post is if I just got it blatantly incorrect or got a small detail wrong that could bite me in the ass later.
Feb 03 · 3 months ago
3 Later Comments ↓
🗡️ The_Jackal [OP, Weapons dealer, possibly mutant killer] · Feb 03 at 23:37:
@jsreed5 I wondered after this, if I were to correct the part about finite terms, would there be anything left that's incorrect? I went ahead and corrected the part about 'coeffecients of variables raised to powers' but left the section regarding x⁰ and x¹ in for myself if I come back confused after sometime and see that as a definition before looking at my notes, because when I first searched I would see definitions like that. So far if I were to summarize it, would 'A polynomial is an algebraic expression which is a sum of terms that only contain the operations of addition, subtraction, multiplication, or exponents. It cannot have negative numbers, variables, fractions, or mixed numbers as exponents nor include the radical sign (square root symbol) or division by a variable' be correct? Excluding a short introduction to degrees, at least. After doing some looking around, I found something about the 'power series' which I heard had things called polynomials but weren't quite polynomials like the ones you're introduced to in introductory algebra.
omg no, don't listen to the infinite guy, polynomials are finite, for the infinite stuff they have a separate name "power series", cause those abominations are so far removed from actual polynomials that it's not funny anymore.
Your stuff is totally correct, I just meant that it's too much information for an intro, like if you were writing a book or something, but if it's notes for an exams it all makes sense. Exams test breadth instead of depth, otherwise most people would fail them and the all them institutions would make no money.
Polynomials are extremely basic, and you can define them with just addition and multiplication and that's all you need to understand them. If it were me, I might've even defined multiplication to really drive the point home how basic we are talking. Now actually putting that on paper in a way you could fight an examiner over its correctness, that's some hard work (and you would need to fight, cause you would get bashed just for going out of line), so yeah, better stick with what you've got there.
👻 darkghost · Feb 04 at 10:12:
Agreed polynomials are pretty simple. They're purposely scope limited to be the format of (number)(variable)^(integer exponent) + (number)(variable)^(integer exponent) + (repeat this pattern a finite number of times)
2x + 4x² + 5x³ + 2x⁴ + 9x⁵ + 5x⁶ - 3x⁷ - x⁸ is an example.
Original Post
I have another math question, and it's if this introduction to polynomials I wrote for myself is any good. The things in parentheses like (positive whole numbers) are for later if I come back to do a quick read-through given my less than stellar memory. A polynomial (from the Greek word poly, meaning many, and the Latin nomial, meaning names or terms) is an algebraic expression which consists of variables (also referred to as indeterminates) and coefficients that only involves the operations...