Show that is a factor of , then factor f(x) completely and find all zeros of the function. Show all algebraic work including synthetic division and factoring steps.

Factored form: f(x) = ()()()

Zeros: x = , ,

Find the volume of the solid whose base is the region bounded by f(x), g(x) and the x-axis on the interval [0, 1], and whose cross-sections perpendicular to the y-axis are squares. your work must show the integral, but you may use your calculator to evaluate it. give 3 decimal places for your answe