Plot a function around a point where there are different left and right limits

Plot[ Abs[x^3-1]/(x-1), {x,-1,3} ]

Look specifically at  how absolute value affects the shape of a function’s graph.

Plot[ Abs[x^3-1], {x,-1,3}]

Mathematica can factor polynomials for you.

Factor[ x^3 - 1 ]