Final answer:
The correct answer is (c) at the x-intercept because a polynomial has a factor of (x - a) if and only if 'a' is a root, which corresponds to the x-intercepts on its graph.
Step-by-step explanation:
To find the factors of a polynomial from its graph, follow this rule: if the number c is a root of a polynomial, then x - c is a factor. The correct answer is (c) at the x-intercept. This is because when a polynomial function crosses the x-axis, the y-value is zero, indicating that the corresponding x-value is a root of the polynomial. For any real number 'a' that is a root, the polynomial will have a factor of (x - a). The maximum and minimum points on a graph, while useful for other analyses, are not directly related to the factors of the polynomial. The y-intercept, which is where the graph crosses the y-axis, gives us the y-value when x is zero, but this does not provide information about the factors of the polynomial unless the y-intercept itself is zero.