Degree 4; zeros: 3i, 8, -8 ....Find the remaining zeros of f

Question

I am so confused algebra 2 is killing me

Answer 1

Remember in the last question, I mentioned that complex zeros have conjugates?  The conjugate of the known complex zero is that missing zeros.

Answer 2

As Michael said... If there is a zero at 3i, there is also a zero at -3i

 

Your 4 zeroes are at: 3i, -3i, 8, -8

If 3i is a zero then (x-3i) is a factor

If -3i is a zero then (x+3i) is a factor

If 8 is a zero then (x-8) is a factor

If -8 is a zero the (x+8) is a factor

 

Your polynomial is found by the product of the factors

 

p(x) = (x-3i)(x+3i)(x-8)(x+8)

p(x) = (x² +9)(x² - 64)

 

Just finish multiplying this out to find the final result