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Prove It If $\displaystyle 5 + 3i$ is a zero, then so is $\displaystyle 5 - 3i$.
So $\displaystyle x - (5 + 3i)$ and $\displaystyle x - (5 - 3i)$ are factors.
Therefore so is $\displaystyle [x - (5 + 3i)][x - (5 - 3i)]$
$\displaystyle = x^2 - x(5 - 3i) - x(5 + 3i) + (5 + 3i)(5 - 3i)$
$\displaystyle = x^2 - 5x + 3ix - 5x - 3ix + 25 + 9$
$\displaystyle = x^2 - 10x + 34$.
So divide your polynomial by $\displaystyle x^2 - 10x + 34$ in order to find the third factor (and third zero).