For any function y = (x), the following hold true. (a) The real solutions of (x) =

For any function y = ƒ(x), the following hold true.

(a) The real solutions of ƒ(x) = 0 correspond to the x-intercepts of the graph.

(b) The real solutions of ƒ(x) < 0 are the x-values for which the graph lies below the x-axis.

(c) The real solutions of ƒ(x) > 0 are the x-values for which the graph lies above the x-axis.

In each exercise, a polynomial function ƒ(x) is given in both expanded and factored forms. Graph each function, and solve the equations and inequalities. Give multiplicities of solutions when applicable.

ƒ(x) = 2x⁴ - 9x³ - 5x² + 57x - 45

ƒ(x) = (x - 3)² (2x + 5)(x - 1)

(a) ƒ(x) = 0 

(b) ƒ(x) < 0

(c) ƒ(x) > 0