Which polynomial function has a leading coefficient of 3 and roots –4, i, and 2, all with multiplicity 1?
f(x) = 3(x + 4)(x – i)(x – 2)
f(x) = (x – 3)(x + 4)(x – i)(x – 2)
f(x) = (x – 3)(x + 4)(x – i)(x + i)(x – 2)
f(x) = 3(x + 4)(x – i)(x + i)(x – 2)

Question

Which polynomial function has a leading coefficient of 3 and roots –4, i, and 2, all with multiplicity 1?
f(x) = 3(x + 4)(x – i)(x – 2)
f(x) = (x – 3)(x + 4)(x – i)(x – 2)
f(x) = (x – 3)(x + 4)(x – i)(x + i)(x – 2)
f(x) = 3(x + 4)(x – i)(x + i)(x – 2)

misty1212 · Answer

http://www.wolframalpha.com/input/?i=expand+3%28x%2B4%29%28x%5E2%2B1%29%28x-2%29

misty1212 · Answer

oh hold on

misty1212 · Answer

if it is supposed to be a real polynomial you have to go with the last one

misty1212 · Answer

each factor is $(x-\text{ one of the zeros})$

misty1212 · Answer

except if it should be real, then you need both $(x-i)$ and $(x+i)$ i would pick D

anonymous · Answer

Thank you!!!

misty1212 · Answer

$$\color\magenta\heartsuit$$

anonymous · Answer

imaginary roots always occur in pairs.