Factor the polynomial and use the factored form to find the zeros. (Enter your answers as a comma-separated list. Enter all answers using the appropriate multiplicities.) \[ P(x)=x^{3}+5 x^{2}-4 x-20 \] Sketch the graph.

To factor the polynomial \( P(x) = x^3 + 5x^2 - 4x - 20 \), you can begin by using synthetic division or the Rational Root Theorem to find possible roots. Upon testing \( x = 2 \), we find that it is a root, allowing us to factor \( P(x) \) as \( (x - 2)(x^2 + 7x + 10) \). Further factoring \( x^2 + 7x + 10 \) gives \( (x + 2)(x + 5) \). Thus, the completely factored form is \( P(x) = (x - 2)(x + 2)(x + 5) \). To find the zeros, set each factor to zero: - \( x - 2 = 0 \) → \( x = 2 \) - \( x + 2 = 0 \) → \( x = -2 \) - \( x + 5 = 0 \) → \( x = -5 \) The zeros of the polynomial are therefore \( 2, -2, -5 \). To sketch the graph, you would plot the points corresponding to the zeros on a coordinate plane: \( (2, 0) \), \( (-2, 0) \), and \( (-5, 0) \). Since the polynomial is cubic with a positive leading coefficient, the graph will start from the bottom left, cross the x-axis at each of the zeros, and continue rising towards the top right, reflecting the behavior of cubic functions.