The polynomial p(x)=x^3-19x-30 has a known factor of (x+2). Rewrite p(x) as a product of linear factors.

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Polynomial Division: First, let's do polynomial division to divide p(x) by (x+2).Set Up Division: Set up the division: (x^3 - 19x - 30) ÷ (x + 2).Divide x^3: Divide x^3 by x to get x^2. Multiply (x + 2) by x^2 to get x^3 + 2x^2. Subtract this from the original polynomial to get -2x^2 - 19x.Divide -2x^2: Now, divide -2x^2 by x to get -2x. Multiply (x + 2) by -2x to get -2x^2 - 4x. Subtract this from -2x^2 - 19x to get -15x.Divide -15x: Next, divide -15x by x to get -15. Multiply (x + 2) by -15 to get -15x - 30. Subtract this from -15x - 30 to get 0.Factor Quadratic: So, the result of the division is x^2 - 2x - 15. Now we need to factor this quadratic.Find Two Numbers: Looking for two numbers that multiply to -15 and add up to -2. Those numbers are -5 and 3.Factor Quadratic: Factor the quadratic to get (x - 5)(x + 3).Linear Factors: Now we have all the linear factors of p(x): (x + 2)(x - 5)(x + 3).

The polynomial $p(x) = x^3 - 19x - 30$ has a known factor of $(x + 2)$ . Rewrite $p(x)$ as a product of linear factors.

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The polynomial p(x)=x3−19x−30 p(x) = x^3 - 19x - 30 p(x)=x3−19x−30 has a known factor of (x+2) (x + 2) (x+2). Rewrite p(x) p(x) p(x) as a product of linear factors.

The polynomial $p(x) = x^3 - 19x - 30$ has a known factor of $(x + 2)$ . Rewrite $p(x)$ as a product of linear factors.