Question

Find the GCD d(x) of the following pairs of polynomials a(x),b(x) in Z3[x]. In each case,...

Find the GCD d(x) of the following pairs of polynomials a(x),b(x) in Z3[x]. In each case, express d(x) as a linear combination of a(x) and b(x).

a) a(x)= x3 + x2 +1 , b(x)= x2+1

b) a(x)= x3 + x2+ 1 , b(x)= x2 + x + 1

c) a(x)= x3 +x2 +1 ,b(x)= x2 + x

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
**NUMBER THEORY** Proof that the following polynomials do not have integer roots. a) x3 − x...
**NUMBER THEORY** Proof that the following polynomials do not have integer roots. a) x3 − x + 1 b) x3 + x2 − x + 1
For each of the following pairs of polynomials f(x) and g(x), write f(x) in the form...
For each of the following pairs of polynomials f(x) and g(x), write f(x) in the form f(x) = k(x)g(x) + r(x) with deg(r(x)) < deg(g(x)). a)   f(x) = x^4 + x^3 + x^2 + x + 1 and g(x) = x^2 − 2x + 1. b)   f(x) = x^3 + x^2 + 1 and g(x) = x^2 − 5x + 6. c)   f(x) = x^22 − 1 and g(x) = x^5 − 1.
a) Use the Euclidean Algorithm to find gcd(503, 302301). (b) Write gcd(503, 302301) as a linear...
a) Use the Euclidean Algorithm to find gcd(503, 302301). (b) Write gcd(503, 302301) as a linear combination of 38 and 49. (c) What is an inverse of 503 modulo 302301? (d) Solve 503x ≡ 2 (mod 302301)
. Rewrite each of the following polynomials, ordering the terms using the lex order, the grlex...
. Rewrite each of the following polynomials, ordering the terms using the lex order, the grlex order, and the grevlex order, giving LM(f), LT(f), and multideg(f) in each case. a. f(x, y,z) = 2x + 3y + z + x2 − z 2 + x3 . b. f(x, y,z) = 2x2 y8 − 3x5 yz4 + xyz3 − xy4 .
1) Determine whether x3 is O(g(x)) for the following: a. g(x) = x2 + x3 b....
1) Determine whether x3 is O(g(x)) for the following: a. g(x) = x2 + x3 b. g(x) = x2 + x4 c. g(x) = x3 / 2 2) Show that each of these pairs of functions are of the same order: a. 3x + 7, x b. 2x2 + x - 7, x2
Q7) Factorise the polynomial f(x) = x3 − 2x2 + 2x − 1 into irreducible polynomials...
Q7) Factorise the polynomial f(x) = x3 − 2x2 + 2x − 1 into irreducible polynomials in Z5[x], i.e. represent f(x) as a product of irreducible polynomials in Z5[x]. Demonstrate that the polynomials you obtained are irreducible. I think i manged to factorise this polynomial. I found a factor to be 1 so i divided the polynomial by (x-1) as its a linear factor. So i get the form (x3 − 2x2 + 2x − 1) = (x2-x+1)*(x-1) which is...
Let p(x) = x2 + x + 2 in Z3 [x]. a) List the distinct cosets...
Let p(x) = x2 + x + 2 in Z3 [x]. a) List the distinct cosets of E = Z3 [x] / <x2 + x + 2> b) Write the addition and multiplication table of E = Z3 [x] / <x2 + x + 2> c) Identify a subfield of E that is isomorphic to Z3 d) Does p(x) have any zeros in E? (Hint: since E is a field, what is the maximum number of zeros p(x) can have...
1. For each of the following pairs of equations, find the x and y values at...
1. For each of the following pairs of equations, find the x and y values at the intersection a) 36=xy and (y)/(x)=(1)/(4) b) 4=x^((1)/(2))y^((1)/(2)) and y/x=1/4 c) a=xy and y/x=b/c d) 48=4x+6y and y/x=2/3
**NUMBER THEORY** Proof that the following polynomials do not have integer roots. a) x3 + x2...
**NUMBER THEORY** Proof that the following polynomials do not have integer roots. a) x3 + x2 − x + 3 b) x5 − x2 + x − 3.
3. (50) Let f(x) = x^4 + 2. Find a factorization of f(x) into irreducible polynomials...
3. (50) Let f(x) = x^4 + 2. Find a factorization of f(x) into irreducible polynomials in each of the following rings, justifying your answers briefly: (i) Z3 [x]; (ii) Q[x] (this can be done easily using an appropriate theorem); (iii) R[x] (hints: you may find it helpful to write γ = 2^(1/4), the positive real fourth root of 2, and to consider factors of the form x^2 + a*x + 2^(1/2); (iv) C[x] (you may leave your answer in...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT