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which of the following options correctly represents the complete factored
form of the polynomial f(x) = x^4 +5x² + 4 ?

F(x) = (x + 2i)(x - 2i)(x + i)(x - i)

Step-by-step explanation:

We have to find the complete factored form of the polynomial

Now, we are going to factorize the polynomial.

So,

⇒

⇒ F(x) = x²(x² + 4) + (x² + 4)

⇒ F(x) = (x² + 4)(x² + 1)

⇒ F(x) = [x² - i²(2)²][x² - i²(1)²] {Where, i is the cube root of unity i.e. i = √(-1)}

⇒ F(x) = (x + 2i)(x - 2i)(x + i)(x - i) (Answer)

aloha~! my name is zalgo and i am here to you out on this amazing day. to answer your question, yes, nonzero numbers can have a greatest common factor and that would be 1. still don't get it? let me considering every number is divisible by 1 and hence every number has 1 as a factor of theirs. so, if 2 nonzero numbers didn't share any gcf (greatest common factor), they would still have a factor in common and that would be 1.

i hope that this ! : p

"stay and stay proud! " - zalgo

(by the way, do you mind marking me as brainliest? i'd greatly appreciate it! mahalo! x3)