How to Find the Function hx = fx * gx if fx = x² + x and gx = 3x?

To find the function h(x) defined as h(x) = f(x) * g(x), we first need to define the given functions:

• f(x) = x² + x
• g(x) = 3x

Now, substituting these functions into the equation for h(x):

h(x) = f(x) * g(x)
     = (x² + x) * (3x)

Next, we distribute (3x) across the terms in (x² + x):

h(x) = 3x(x²) + 3x(x)
     = 3x³ + 3x²

Therefore, the function h(x) is:

h(x) = 3x³ + 3x²

We can simplify this further by factoring out the common term:

h(x) = 3x²(x + 1)

So, the final result for the function h(x) is:

h(x) = 3x²(x + 1)

This completes our calculation of the function h(x).