How do you find all the zeros of $x^3 + x^2 + 9x + 9$ given zero 3i?

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Answer 1 · 2016-05-21T19:30:04

The zeros are $-1$ , $3i$ and $-3i$ .

We don't really need to be told that $3i$ is a zero, except that it does inform us that we should include Complex zeros in the answer.

This cubic factors by grouping:

$x^3+x^2+9x+9$

$=(x^3+x^2)+(9x+9)$

$=x^2(x+1)+9(x+1)$

$=(x^2+9)(x+1)$

$=(x-3i)(x+3i)(x+1)$

So the zeros are $-1$ , $3i$ and $-3i$ .

How do you find all the zeros of x^3 + x^2 + 9x + 9 x^3 + x^2 + 9x + 9 given zero 3i?