# algebraic

5. ### Real Algebraic Curves

I am reading C. G. Gibson's book: Elementary Geometry of Algebraic Curves. I need some help with aspects of Example 1.4 The relevant text from Gibson's book is as follows: Question 1 In the above text, Gibson writes the following: " ... ... Then a brief calculation verifies that any...
6. ### Affine Algebraic Curves - Kunz - Theorem 1.3

I am reading Ernst Kunz book, "Introduction to Plane Algebraic Curves" I need help with some aspects of Kunz' proof of Theorem 1.3 ... The relevant text from Kunz is as follows: In the above text we read the following: " ... ... Therefore let p > 0. Since a_p has only...
7. ### Affine Algebraic Curves - Kunz - Definition 1.1

I am reading Ernst Kunz book, "Introduction to Plane Algebraic Curves" I need help with some aspects of Kunz' Definition 1.1. The relevant text from Kunz' book is as follows: In the above text, Kunz writes the following: " ... ... If K_0 \subset K is a subring and \Gamma = \mathscr{V}...
8. ### Affine Algebraic Curves - Kunz - Exercise 1 - Chapter 1

I am reading Ernst Kunz book, "Introduction to Plane Algebraic Curves" I need help with Exercise 1, Chapter 1 ... Indeed ... I am a bit overwhelmed by this problem .. Exercise 1 reads as follows: Hope someone can help ... ... To give a feel for the context and notation I am providing...
9. ### Need help verifying answer to algebraic division problem

A problem asks to divide 3x3 - 20x2 + 39x - 18 by x2 - 6x + 9 The answer given is 3x-2 But I found that answer but with a remainder of -6x Can someone help check my answer?
10. ### Algebraic Expression Calculator

This has been the culmination of 1.5 years of work from suggestions and problems by people who struggle with algebraic expressions. Algebraic Expressions Calculator Some examples below where any letter can be used for say n or x and any number where you see a number used Fifteen less than...
11. ### How to underline seperate algebraic terms?

Hello all, I'm doing my end of year math assignment, and it's my first time using Latex. My question regards underlining terms in algebraic expressions. In my textbook, they are underlined like this: Is there any way I can do this using Latex? I tried using \underline{+4a} \underline{+c}...
12. ### What is this algebraic expression?

Hi, It's been a while since I've practiced algebra, and I've forgotten some things. For example, what does it mean when two variables are listed as one on top of the other and they are bounded by a single parentheses? So they look a little like this: (a b) That is, a is on...
13. ### Algebraic expression

Part b... Was not able to continue after getting 36(x-y) Pls help... Thanks.
14. ### Proof of an algebraic theorem

I have introduced to the following algebraic theorem while learning the method of partial fraction. Any polynomial can be written as the product of linear factors and irreducible quadratic factors I need very clear explanation so that I can understand the proof with intuition.
15. ### What's an algebraic curve's polar line for?

I asked this over on mathexchange, but nobody answered, so I'm trying again here. Essentially, I suspect that given an algebraic curve, there is some link between its polar curve, and its dual. But I only know that because someone said so on Wiki; I have no idea what that link actually is :( The...
16. ### Solving an algebraic fraction for x

Hello, Can anyone help me with this? I am using the Chain Rule in Differentiation to differentiate an expression, and I think I have done that OK, but my question goes on to ask for the stationary point which I should be able to find by setting my derivative to equal to 0 and then solve for x...
17. ### Trying to simplify an algebraic fracion

I don't understand how to simplify this simple algebraic fraction and this is the answer given: 1 - \frac{1}{x} = \frac{x - 1}{x} Can anyone tell me how that problem was solved?
18. ### General DE from algebraic equation

Given an algebraic equation (a function), is possible to know which DE this function satisfies? For example, the quadratic function satisfies y'''=0.
19. ### Write trig expression as an algebraic expression containing u and v

I'm stuck on this one: Cos(tan^-1u+tan^-1v) I know you can use cos(a+b)=cosacosb-sinasinb but not sure what to do after.