Q:

How on earth do you graph $2 x^3 - 3 x^2 - 36 x + 7$ by hand?

I found this equation in a maths textbook that asked me to graph it, so to do so I tried to factor it. I used two different online calculators that couldn't do it either. 
But I graphed it on Mathematica on turns out you can graph it?

A:

Obviously you can graph it; it's a polynomial and polynomials can be graphed! If you can't factorise it directly, add a constant to it until it can be factorised, then shift that graph by the value of the constant. In your case, graphing $2x^3-3x^2-36x=x(2x^2-3x-36)$, which can be factorised easily to find the roots and thus a sketch. Once you have your graph, simply shift it upwards by $+7$ to get your original function.

