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Answer :
Final answer:
The factored form of P(x) is (x - 3i)(3x^4 - 20ix^3 + 43x^2 - 291ix + 630 - 999i).
Explanation:
To factor the polynomial P(x), we start by using the given information that 3i is a zero. This means that (x - 3i) is a factor of P(x). To find the remaining factors, we can use polynomial long division or synthetic division.
Let's use synthetic division to divide P(x) by (x - 3i):
The quotient is 3x^4 - 20ix^3 + 43x^2 - 291ix + 630 - 999i.
Now, we have factored P(x) as (x - 3i)(3x^4 - 20ix^3 + 43x^2 - 291ix + 630 - 999i).
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