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F(x) = x^3 + x^2 + 9x + 9 Find all zeros including irrational and/ or complexFactor f completely into linear factors Part of it completed: The zeros are -1, 3i, and -3i

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Given:


F\left(x\right)=x^3+x^2+9x+9

To find:

The zeros

Step-by-step explanation:

Factorizing by grouping method,


\begin{gathered} F\left(x\right)=x^3+x^2+9x+9 \\ =x^2(x+1)+9(x+1) \\ =(x+1)(x^2+9) \end{gathered}

The zeros are found by equating the factors with zero.


\begin{gathered} x+1=0 \\ x=-1 \end{gathered}

And we have,


\begin{gathered} x^2+9=0 \\ x^2=-9 \\ x=\pm√(-9) \\ x=\pm3i \end{gathered}

So, the zeros are,


-1,3i,-3i

Final answer:

The zeros are,


-1,3i,-3i
User Mohammad Fatemi
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