Question

A fourth degree polynomial equation is shown below.

Answer 1

4x^2-8x-12 =
(x -3) * (x +1)

4x^2-24x+32
(x -4) * (x -2)

Factored Form
(x -3) * (x +1) * (x -4) * (x -2) = 0

x = 3
x = -1
x = 4
x = 2

All four roots are real numbers and so the graph crosses the x-axis four times.  The graph of the equation would resemble a "W".