ind the zeros of the polynomial function, and state the multiplicity of each. \( (x)=-4(x+4)(x+4)(x+4)(x-2) \)

To find the zeros of the polynomial function \( f(x) = -4(x+4)^3(x-2) \), we set \( f(x) = 0 \). The factors give us the zeros: \( x + 4 = 0 \) leads to \( x = -4 \) with a multiplicity of 3 (since it's cubed), and \( x - 2 = 0 \) leads to \( x = 2 \) with a multiplicity of 1. So, the zeros are \( x = -4 \) (multiplicity 3) and \( x = 2 \) (multiplicity 1). Now, to visualize these zeros, you can think of them as the points where the graph of the polynomial touches or crosses the x-axis. The zero at \( x = -4 \) will create a 'bump' in the graph due to its odd multiplicity, while \( x = 2 \) will simply cross the axis. If you were to sketch this function, you would see it hugging the x-axis three times at -4 before rising from the axis at 2.