Answer :
Final answer:
To write the polynomial P(x) in factored form, we need to determine the other zeros given that 3i is a zero. Using polynomial long division, we can divide P(x) by (x - 3i)(x + 3i) to obtain a quadratic expression. The quadratic expression can then be factored to find the remaining zeros.
Explanation:
To write the polynomial P(x) in factored form, we need to determine the other zeros given that 3i is a zero. Since complex zeros always come in conjugate pairs, the other zero will be -3i.
To find the factors, we can write P(x) as a product of (x - zero). Therefore, P(x) = 3(x - 3i)(x + 3i)(x - a)(x - b)(x - c), where a, b, and c are the remaining zeros to be determined.
Using polynomial long division, we can divide P(x) by (x - 3i)(x + 3i) to obtain a quadratic expression. The quadratic expression can then be factored to find the remaining zeros.
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