Final answer:
The polynomial function that represents a graph in factored form is determined by the roots indicated by where the graph intersects the x-axis, their multiplicities, and the sign of the leading coefficient. Without the actual graph, the correct form cannot be determined from the options provided.
Step-by-step explanation:
To determine which polynomial function in factored form represents the given graph, we need to identify the roots (or zeros) of the polynomial and their corresponding multiplicities based on the graph. The graph would show where the function crosses the x-axis, indicating the roots. With the correct zeroes, it's then important to consider the multiplicity of each zero (whether the graph touches and turns around at a zero, indicating an even multiplicity, or crosses through the x-axis at a zero, indicating an odd multiplicity), and the leading coefficient, which can be positive (if the ends of the graph are pointing in opposite directions) or negative (if the ends of the graph are pointing in the same direction).
Without the actual graph provided, we can't definitively select the correct polynomial function from the options given. However, to aid in understanding, if the graph had roots at -2, 1, and -1, with the end behavior of the graph suggesting a negative leading coefficient (e.g., both ends of the graph pointing downwards), the correct factored form could be y = -a(x + 2)(x - 1)(x + 1), where a is a positive constant defining the vertical stretch or compression of the polynomial.