Consider the following graph of Px a Find all the real zeros

Consider the following graph of P(x). (a) Find all the real zeros of P(x). (b) Assuming P(x) has only real zeros, and that the leading coefficient is 1, what is P(x)? Leave answer factored, DO NOT EXPAND.

Solution

From the graph of the function, it is apparent that the real zeros of P(x) are x = -3, x = 0, x = 2 and x = 9.

If the leading coeffficient is 1, then P(x) = x(x +3)(x - 2)(x - 9)