The graph of the polynomial f(x) is given below. If f(x) has degree 3, find the factored equation for f(x).

A coordinate plane has a horizontal x-axis labeled from negative 2 to 6 in increments of 1 and a vertical y-axis labeled from negative 3 to 4 in increments of 1. From left to right, a curve labeled f left-parenthesis x right-parenthesis, rises at a decreasing rate, passing through the point left-parenthesis 0 comma negative 1 right-parenthesis to a relative maximum at left-parenthesis 1 comma 0 right-parenthesis, then falls to a relative minimum at left-parenthesis 3 comma negative 1 right-parenthesis, and then rises at an increasing rate, passing through the point left-parenthesis 4 comma 0 right-parenthesis.

Select the correct answer below:

f(x)=14(x+1)2(x+4)

f(x)=−116(x+1)2(x+4)

f(x)=14(x−4)(x−1)2

f(x)=−116(x−4)(x−1)2

f(x)=116(x+1)2(x+4)

f(x)=−14(x−4)(x−1)2