Question

Consider the expressions x+1, 2x-3, and 4x+1.

A. Create a new function, h(x), that is the product of these three expressions.
B. Sketch a graph of h(x)
C. How does this function demonstrate the Fundamental Theorem of Algebra?

Answer 1

The new function h(x) is h(x) = 8x³ - 2x² - 13x - 3

The graph is attached

This function demonstrate the fundamental theorem of algebra by being a non-constant polynomial

Creating a new function h(x)

From the question, we have the following parameters that can be used in our computation:

x + 1, 2x - 3, and 4x + 1

The product of these three expressions is the function h(x)

So, we have

h(x) = (x + 1) * (2x - 3) * (4x + 1)

When expanded, we have

h(x) = 8x³ - 2x² - 13x - 3

The graph of h(x) is added as an attachment

This function demonstrate the fundamental theorem of algebra by being a non-constant polynomial, and its roots are the solutions to the equation h(x) = 0, representing the points where the graph of h(x) intersects the x-axis.