2. factor f(x) = x4 + x3 – 8x2 + 6x + 36 completely. then sketch the graph.

The complete factorization of f(x) = x4 + x3 – 8x2 + 6x + 36 is f(x) = (x+2) (x+3) (x^2-4x+6).

See attached picture for the sketch of the graph of the function. To sketch the graph, simply substitute values of x into the function in order to get its specific values of f(x) = y. Plot these values in the cartesian plane. I hope this helped you a lot.