Problem

Consider the following polynomial.
\[
F(x)=x^{3}+8 x^{2}+9 x-18
\]

Step 3 of 3 : Using your answers to the previous steps, polynomial division, and the quadratic formula, f necessary, find all of the zeros of the polynomial. Include multiples of the same zero where applicable.
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Answer

Final Answer: The zeros of the polynomial are \(\boxed{1, -3, -6}\).

Steps

Step 1 :The given polynomial is \(F(x)=x^{3}+8 x^{2}+9 x-18\).

Step 2 :We are asked to find the zeros of the polynomial. The zeros of a polynomial are the values of x that make the polynomial equal to zero.

Step 3 :We can start by trying to factor the polynomial. If that's not possible, we'll have to use the cubic formula or numerical methods to find the roots.

Step 4 :Upon factoring, we find that the polynomial factors into \((x - 1)*(x + 3)*(x + 6)\).

Step 5 :This means that the zeros of the polynomial are \(x = 1\), \(x = -3\), and \(x = -6\). These are the values of x that make the polynomial equal to zero.

Step 6 :Final Answer: The zeros of the polynomial are \(\boxed{1, -3, -6}\).

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