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.

Factor the expression \( x^{3}+5x^{2}-4x-20 \). Factor the expression by following steps: - step0: Factor: \(x^{3}+5x^{2}-4x-20\) - step1: Rewrite the expression: \(x^{2}\times x+x^{2}\times 5-4x-4\times 5\) - step2: Factor the expression: \(x^{2}\left(x+5\right)-4\left(x+5\right)\) - step3: Factor the expression: \(\left(x^{2}-4\right)\left(x+5\right)\) - step4: Factor the expression: \(\left(x-2\right)\left(x+2\right)\left(x+5\right)\) The factored form of the polynomial \( P(x) = x^{3} + 5x^{2} - 4x - 20 \) is \((x-2)(x+2)(x+5)\). To find the zeros of the polynomial, we set each factor equal to zero and solve for \( x \): 1. \( x - 2 = 0 \) gives \( x = 2 \) 2. \( x + 2 = 0 \) gives \( x = -2 \) 3. \( x + 5 = 0 \) gives \( x = -5 \) Therefore, the zeros of the polynomial are \( x = 2, -2, -5 \). To sketch the graph, we can plot these zeros on the coordinate plane and determine the behavior of the polynomial between these points. Since the polynomial is of degree 3, it will have a local maximum or minimum at one of the zeros. The graph will be a cubic curve that opens upward or downward.