Question

A fourth degree polynomial equation is shown below.

(4x^2-8x-12)(4x^2-24x+32)=0

Use this problem to answer the following questions.


1) Write the polynomial equation in factored form.

2) Find the solutions of the polynomial equation.

3) Discuss the zeros of the graph of the polynomial equation y=(4x^2-8x-12)(4x^2-24x+32) and how many times the graph of the equation intersects the x-axis

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".