we use the definition of
associates in a ring
Let p(x) = x2 + 3x + 1 ∈ Z5[x] and let (p) ▹ Z5[x] be the principal ideal generated by p. Put K = Z5[x]/(p). For f(x)=x2−1∈ Z5[x] and g(x)=x2+1∈Z5[x] find a,b∈Z5 such that (f + (p))(g + (p)) = a + bx + (p) in K.
- (5 points) Find all the solutions in Z5 of the equation 3 – T –ī=.
(5) Let Ф, : Z5[x] Zg denote the evaluation homomorphism at r Zg Find a nonzero polynomial of smallest degree which in kernel of all φ-for r 0,1,2,3,4
(5) Let Ф, : Z5[x] Zg denote the evaluation homomorphism at r Zg Find a nonzero polynomial of smallest degree which in kernel of all φ-for r 0,1,2,3,4
Find all rational zeros of the function f(x)=2x'-9x'-6x+5.
Find all rational zeros of the function f(x)=2x'-9x'-6x+5.
Show that x^3+x^2+1 is irreducible 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...
(1 point) Evaluate the indefinite integral. cos(/z5) Integral NOTE: Enter arctan(x) for tan-1 z, sin(x) for sin .] to enter all necessary, ( and)!!
(1 point) Evaluate the indefinite integral. cos(/z5) Integral NOTE: Enter arctan(x) for tan-1 z, sin(x) for sin .] to enter all necessary, ( and)!!
(5) Let Ф, . Ž5Įx] 25 denote the evaluation homomorphism at r є z5. Find a nonzero polynomial of smallest degree which in kernel of all Φ, for r 0, 1,2,3,4.
(5) Let Ф, . Ž5Įx] 25 denote the evaluation homomorphism at r є z5. Find a nonzero polynomial of smallest degree which in kernel of all Φ, for r 0, 1,2,3,4.
Find all solutions of the following: cos(2x)+3cos(x)=-2
cos(2x) + 3 cos(x) = -2 9. Find all solutions of the following:
For y = f(x) = 2x - 1, x = 5, and △x = 3 find a) △y for the given x and △x values, b) dy = f'(x)dx, c) dy for the given x and △x values.