Posted by **Piggy** on Friday, April 5, 2013 at 12:23am.

write a fourth degree polynomial function a leading coefficient o 1 given three of its zeros are -1, 3 and 2i, then re-write it in simplified form.

- Algebra II -
**Reiny**, Friday, April 5, 2013 at 1:30am
The key concept here is that imaginary numbers always appear as conjugates

so if 2i is a zero, so is -2a

so we would have x = ±2i

x^2 = 4i^2

x^2 = -4

so x^2 + 4 is a factor

the polynomial is

f(x) = (x+1)(x-3)(x^2 + 4)

I will leave it up to you to expand it, but I would consider the factored form more simplified than the expanded form.

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