what must be a factor of the polynomial function f(x) graphed on the coordinate plane below?\no x - 6\no x…

Explanation:

Step1: Recall factor - root relationship

If (x = a) is a root of the polynomial function (y = f(x)), then ((x - a)) is a factor of (f(x)). The roots of a polynomial function are the (x) - intercepts of its graph.

Step2: Identify (x) - intercept

From the graph, we see that the polynomial function (f(x)) intersects the (x) - axis at (x=-6).

Step3: Determine the factor

Since (x=-6) is a root (i.e., (f(-6)=0)), then (x + 6) is a factor of the polynomial function (f(x)) (because if (x=-6), then (x+6=0)).

Answer:

(x + 6)