1- What are the units in Z? What are the units in F[x]? Don’t write out a formal proof, but discuss why. 2- What is the analogy between Z and F[x]? 3- Let p(x) = x^3 + 3x + 1 = (x+3)^2 * (x+4) in Z5[x...

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1- What are the units in Z? What are the units in F[x]? Don’t write out a formal proof, but discuss why. 2- What is the analogy between Z and F[x]? 3- Let p(x) = x^3 + 3x + 1 = (x+3)^2 * (x+4) in Z5[x...

1- What are the units in Z? What are the units in F[x]? Don’t write out a formal proof, but discuss why.

2- What is the analogy between Z and F[x]?

3- Let p(x) = x^3 + 3x + 1 = (x+3)^2 * (x+4) in Z5[x].

(a) Perform the following computation in Z5[x]/(p(x)). Give your answers in the form [r(x)] where r(x) has degree as small as possible.

i. [4x] + [3x^2 + x + 2]

ii. [x^2][2x^2+1]

(b) Show that Z5[x]/((p(x)) has zero divisors.

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Answer 1

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Answer #1

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1- What are the units in Z? What are the units in F[x]? Don’t write out a formal proof, but discuss why. 2- What is the analogy between Z and F[x]? 3- Let p(x) = x^3 + 3x + 1 = (x+3)^2 * (x+4) in Z5[x...

Homework Answers

Add Answer to:
1- What are the units in Z? What are the units in F[x]? Don’t write out a formal proof, but discuss why. 2- What is the analogy between Z and F[x]? 3- Let p(x) = x^3 + 3x + 1 = (x+3)^2 * (x+4) in Z5[x...

Let f(x)= -3x^4+79x^2-3x+1/ 5x^4+19x^3+2x+5

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Let g: R→R be a polynomial function of even degree and let B={g(x)|x ∈R} be the range of g. Define g such that it has AT LEAST TWO TERMS G(x) - 1 - 3x^2 1. Using the properties and definitions of the...

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1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) an...

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1- What are the units in Z? What are the units in F[x]? Don’t write out a formal proof, but discuss why. 2- What is the analogy between Z and F[x]? 3- Let p(x) = x^3 + 3x + 1 = (x+3)^2 * (x+4) in Z5[x...

Homework Answers

Add Answer to: 1- What are the units in Z? What are the units in F[x]? Don’t write out a formal proof, but discuss why. 2- What is the analogy between Z and F[x]? 3- Let p(x) = x^3 + 3x + 1 = (x+3)^2 * (x+4) in Z5[x...

Add Answer to:
1- What are the units in Z? What are the units in F[x]? Don’t write out a formal proof, but discuss why. 2- What is the analogy between Z and F[x]? 3- Let p(x) = x^3 + 3x + 1 = (x+3)^2 * (x+4) in Z5[x...