Problem 4. Consider the field Z2[x]/(F), where $ = x5 + x2 + 1. In this...
Problem 4. Consider f(x) = x5+ x4 + 2x3 + 3x2 + 4x + 5 ∈ Q[x] and our goal is to determine if f is irreducible over Q. We compute f(1), f(−1), f(5), f(−5) directly and see that none of them is zero. By the Rational Roots Theorem, f has no root in Q. So if f is reducible over Q, it cannot be factored into the product of a linear polynomial and a quartic polynomial (i.e. polynomial of...
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
(1 point) This problem will illustrate the divergence theorem by computing the outward flux of the vector field F x, y, z = 2ī + 4j + k across the boundary of the right rectangular prism: 1 sx <5,-2 Sys3,-33z37 oriented outwards using a surface integral and a triple integral over the solid bounded by rectangular prism. Note: The vectors in this field point outwards from the origin, so we would expect the flux across each face of the prism...