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Answer :
Final answer:
The factored form of P(x) is (x - 4i)(x + 4i)(3x^3 - 60x^2 + 320).
Explanation:
To write the polynomial P(x) = 3x^5 - 5x^4 + 36x^3 - 60x^2 - 192x + 320 in factored form, we need to find all the zeros of the polynomial. Given that 4i is a zero, we know that its conjugate -4i is also a zero, since complex zeros occur in conjugate pairs. So, we have two zeros: 4i and -4i. By the Factor theorem, we can express the polynomial as a product of linear factors by considering these zeros. Thus, the factored form of P(x) is: P(x) = (x - 4i)(x + 4i)(3x^3 - 60x^2 + 320).
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