In order to find a root of a(x) in a finite field F, the simplest method...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
In order to find a root of a(x) in a finite field F, the simplest method (if F is small) is to test every element of F by substitution into the equation a(x) = 0. 1 Find all the roots of the following polynomials in z 5[x], and factor the polynomials: x³+x²+x+1; 3x4+x²+1; x³+1; 4+1; 4+4 In order to find a root of a(x) in a finite field F, the simplest method (if F is small) is to test every element of F by substitution into the equation a(x) = 0. 1 Find all the roots of the following polynomials in z 5[x], and factor the polynomials: x³+x²+x+1; 3x4+x²+1; x³+1; 4+1; 4+4
Expert Answer:
Answer rating: 100% (QA)
To find the roots of each polynomial in Zx we simply substitute every element of Z into polynomial a... View the full answer
Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
Posted Date:
Students also viewed these mathematics questions
-
Let F be an algebraic closure of the field Q of rational numbers and let E F be a splitting field over Q of the set S = { x 2 + a | a Q} so that E is algebraic and Galois over Q (Theorem 3.11). (a)...
-
In 1224, Leonardo of Pisa, better known as Fibonacci, answered a mathematical challenge of John of Palermo in the presence of Emperor Frederick II: find a root of the equation x3 +2x2 +10x = 20. He...
-
Use the following financial statements to answer to answer the questions: Income Statement 2021 Sales Cost of Goods Sold Depreciation EBIT Interest Taxable Income Taxes (40%) Net Income Dividends...
-
In Exercises 1318, find the average rate of change of the function from x 1 to x 2 . f(x)=x from x = 4 to x = 9
-
Write a paper on Individual Postings addressing the following. Marketers find many opportunities by identifying trends (directions or sequences of events that have some momentum and durability) and...
-
Describe how you would obtain, free of charge, a law review article from the Buffalo Criminal Law Review.
-
At the end of 2005, a parent company, P plc, with one subsidiary had a holding representing 10% of the equity of R Ltd, a clothing company. It had cost 80,000 when purchased at the start of 2004. At...
-
The financial condition of White Co. Inc. is expressed in the following accounting equation: Required a. Are dividends paid to creditors or investors? Explain why. b. How much cash is in the Retained...
-
QUESTION 3 (25 MARKS) Star Sdn Bhd produces limited-edition stainless-steel wok which is sold to restaurants and other users. Each wok is sold at RM89 per unit and the budgeted normal production per...
-
On January 1, 2024, Perry Company purchased 8,000 shares of Soho Companys common stock for $120,000. Immediately after the stock acquisition, the statements of financial position of Perry and Soho...
-
You borrow $15000 and repay monthly over the next five years. Interest is set at 2% per month. Monthly payments are $431.5195. A lump sum payment of $2000 as well as a regular payment was paid at the...
-
listen to the This American Life audio clips. 1. In the opening clip, reporter Jacob Goldstein is trying to understand where all the lost money went during the financial crisis. He asks his business...
-
1-2 3 3 02 1. Let A = and B = find 2A-3B. 45-6 7 1 8 2 1 [1-2 -5 2. Given A= 1 0 and B find 3 40 3 4 a. AB b. BA
-
Determine a business for the group to start Option. Do a SWOT analysis on the business and the team members Option. Each team member selects two factors that help make up a business plan and explains...
-
Using online sources explain (using quotes) the following concepts as they relate to economics, then interpret each one after the quotation marks what is equibrium? when does it happen? what is...
-
The number of visits to public libraries increased from 1.4 billion in 1997 to 1.6 billion in 2001 . Find the average rate of change in the number of public library visits from 1997 to 2001.
-
a. The 7.6%, twenty-year bond yields 5.6%. If this yield to maturity remains unchanged, what will be its price one year hence? Assume annual coupon payments and a face value of $1,000. b. What is t...
-
Tiger, Inc. signed a lease for equipment on July 1, 2007.The lease is for 10 years (the useful life of the asset).The first of 10 equal annual payments of $500,000 was made on July 1, 2007.The...
-
Give an example of a finitely generated field extension, which is not finite dimensional.
-
If H is a normal subgroup of order p k of a finite group G, then H is contained in every Sylow p-subgroup of G.
-
Proof that F is a splitting field over K of a finite set { 1 ... , n ) of polynomials in K[x] if and only if Fis a splitting field over K of the single polynomial = 1 2 n .
-
In Caroline Company, total material costs are \($48,000\), and total conversion costs are \($60,000\). Equivalent units of production are materials 10,000 and conversion costs 12,000. Compute the...
-
Sota Company has the following production data for April: units transferred out 40,000, and ending work in process 5,000 units that are 100% complete for materials and 40% complete for conversion...
-
Motta Company has the following production data for April: units started and completed 40,000, and ending work in process 5,000 units that are 100% complete for materials and 40% complete for...
Study smarter with the SolutionInn App