I have two questions on this topic. The first one is finding the x3+2 as a product of linear factors in Z3[X]. I have in my notes that -
x3+2=x3-1 (in mod 3)
The part of this I dont get is the second and third step. How do we go from x3-1 to (x)3-(1)3=(x3-1)(x2+x+1)?
The second question is to show 2x3+3x-7x-5 as a product of linear factors in Z1[x]. I keep running into polynomials that cant be factored. I presume the step Im missing is just like the previous question where i need to use the properties of mod, but Im not sure how/where to do it?