Hello,
I need help with all parts of Problem 13 (a and b).
Please show all the steps and the solutions of the problem.
Thank you very much.
Hello, I need help with all parts of Problem 13 (a and b). Please show all...
Polynomial over the Fields: a) If p(x) an element of F[x] is not irreducible, then there are at least two polynomials g(x) and h(x), neither which is a constant, such that p(x)=g(x)h(x). Explain b) Use problem a to prove: If p(x) is not irreducible, then p(x)=j(x)k(x), where both j(x) and k(x) are polynomials of lower degree than p(x).
Hello, I need help with this problem. Please show the solution and all the steps that lead to it. Thank you very much. or ts A and
Hello, I need help with Problem 3. Please show all the steps and the solutions of the problem. Thank you very much. 3. Compute the hyperbolic area of the hyperbolic triangle shown below: 3. Compute the hyperbolic area of the hyperbolic triangle shown below:
Hello, I need help with Problem 4. Please show all the steps and the solutions of the problem. Thank you very much. 4. Show that the image of the upper half plane H2 z E C: 3(2) > 0) under the map C(z) =-i is the disk D-{z E C : 려 < 1].
Hello, I need help with Problem 4. Please show all the steps and the solutions of the problem. Thank you very much. 4. (10 points) Compute the images of the lines it : t 0 and it: R} under the map C(z) = 2-2 IE 2+i 4. (10 points) Compute the images of the lines it : t 0 and it: R} under the map C(z) = 2-2 IE 2+i
Let F=Z_3 , the finite field with 3 elements. Let f(x) be an irreducible polynomial in F[x]. Let K=F[x]/(f(x)). We know that if r=[x] in K, then ris a root of f(x). Prove that f(r^3) is also a root of f(x). Which of the following are relevant ingredients for the proof? If a and b are in Z_3 then (a+b)^3=a^3+b^3 If g is an automorphism of K leaves g(r) is a root of f(x) The Remainder Theorem The Factor Theorem...
Let F=Z_3, the finite field with 3 elements. Let f(x) be an irreducible polynomial in F[x]. Let K=F[x]/(f(x)). We know that if r=[x] in K, then ris a root of f(x). Prove that f(r^3) is also a root of f(x). Which of the following are relevant ingredients for the proof? If a and b are in Z_3 then (ab)^3=(a^3)(b^3) The Remainder Theorem If a and b are in Z_3 then (a+b)^3=2^3+b^3 For all a in Z_3, a^3=a The first isomorphism...
Hello, I need help with Problem 2. Please show all the steps and the solutions of the problem. Thank you very much. 2" (10 points) Show that the image of the upper half plane H2-(2 E C : S(z) > 0} under the map C(z) = i is the disk D-{2E C : 2ti 2" (10 points) Show that the image of the upper half plane H2-(2 E C : S(z) > 0} under the map C(z) = i is...
Hello, I need help with Problem 1. Please show all the steps and the solutions of the problem. Thank you very much. l. Consider the geode ie L = {it : t E R, t > 0) in 2, and consider the point i+1 which is not on L. Show that there are infinitely many distinct hyperbolic geodesics passing through w that do not intersect L. l. Consider the geode ie L = {it : t E R, t >...
Hello, I need help with the following Discrete problem. Please show your work, thank you! 12. Select a theta notation from among (1), (n), (n?), (nº), (n), (2"), or (n!) for each of the expressions (a) 4n + 2n? -5 (b) 13 + 2 +...+ n (c) Prove you are correct for both parts a and b above