Abstract Algebra Answers

Factorize polynomial x5 + 2x4 + x2 + 2x + 2 over Z/3Z

Prove that in principal ideal ring for every pair of elements exists their GCD.
Prove that if d=GCD(a,b), then there are such elements u,v that d=au+bv.

Prove that next ring is not factorial: R=Z[sqrt(10)]

Is Z[sqrt(-5)] factorial ring?

Show that invertible elements form a group in any associative ring.

Show that set of points (x,x^3) where x is any real form abelian group under + operation
defined as p+q is third point of intersection or tangent line.

-15v + 12v + 17v – -7 = -7

dora decided to buy the tent in a nearby small merchandise store with four doors where she could enter. in how many ways can she enter and exit from the store if she could use different doors

A student is taking a 5 question T/F test. If the student chooses answers at random, what is the probability of getting all questions correct? I'd like to know the formula to solve.