Question

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

Answer 1

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`