What are the irreducible elements of C[x,y]?
359378
This is the ring of polynomials in two variables with complex coefficients. First figure out what the units are (the scalars). An irreducible will be a polynomial p such that if p=fg, then either f or g is a unit. Clearly x and y are irreducible since if x=f(x,y)g(x,y), then either f or g will be a scalar polynomial.
956578
x^2+3x-y=c\n2x +3 -y'=0\ny'= 2x +3\n\n(remember y^0=1)!
396588
If one considers C as a 2-dimensional vector space over R (this is the complex plane representation of complex numbers), then it is trivially isomorphic to R^2 (the real plane) by mapping the complex number (a, b) to the real pair (a, b). The vector space structure is trivially preserved (with respect to real-linear morphisms). If it was not isomorphic, there would be no complex plane representation and we'd be stuck working with an exotic 1-dimensional structure. See http://mathworld.wolfram.com/ComplexPlane.html and http://en.wikipedia.org/wiki/Complex_numbers#Real_vector_space .
576001
By the transitive property, a=c
244218
http://mathworld.wolfram.com/GaloisGroup.html\n\nI'm not sure if I can give you the exact answer since I'm trying to understand it myself.  \nWhat you want is the Galois group of Q(r1, r2, r3, r4, r5) over Q where the ri are the roots to the polynomial x^5 + x + 1.  This group is going to be a subgroup of the group of permutations on 5, but I don't know if I can say anything else about it since x^5 + x + 1 is an irreducible polynomial in Q.  \nHope this helps.
849111
ydy=2xdx\n\n(y^2)/2=x^2+c\n\ny^2=2x^2+d\n\n1=2•3^2+d\n\nd=-17\n\ny^2=2x^2-17\n\ny=±√(2x^2-17)
745882
C is correct but not complete... only the 3 is factored out... the real answer would be:\n\n3(x-1)(x+4)
985975
take - common\n -(y^2-9y+20)\n-(y^2-5y-4y+20)\n-(y(y-5)-4(y-5))\n-(y-4)(y-5)
464936
Commutative operation.
215876
Additive equivalence is a symmetric relation over the reals. See the source link.
417188
y=Asin(2x)+Bcos(2x)+(x/4)\n\nNow you get to determine why.
819588
number of atoms (of each element) on one side equals the other side.
387063
X=[-(30y-433)]/1232\nY=[-(1232x-433)]/30
739570
d2 - =int(c2/10)\n\neasy
492690
S(I)+3f (g)--> SF (g)\n..........2...........6
971807
(0,0)\n(3,0)\ndraw the graphs and then find them out!\nif u can't, then mail me!
316569
y = mx + c\n(0) = (2)(-1) + c\nc = 2\n\ntherefore y = 2x + 2