Which statement describes the graph f(x)=4x^7+40x^6+100x^5?

Graph crosses the x-axis at x = 0 and has zeros at {-5, -5}.

Step-by-step explanation:

Note that f(x) factors as follows:  f(x) = 4x^5 (x^2 + 10x + 25), which in turn factors into f(x) = 4x^5 (x + 5)^2.

To find the zeros, we set this f(x) = to 0 and solve for x:

{0, -5, -5}.

Thus, we can immediately eliminate the first two possible answers.

The factor x^5 tells us that the graph crosses the x-axis at 0.  If we had x^6, which is an even power of x, the graph would only touch the x-axis at 0.

The correct answer choice is the third one.