Respuesta :
Answer:
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
[tex]F(x) = x^{4} + 5x^{2} + 4[/tex]
Now, we are going to factorize the polynomial.
So, [tex]F(x) = x^{4} + 5x^{2} + 4[/tex]
⇒ [tex]F(x) = x^{4} + 4x^{2} + x^{2} + 4[/tex]
⇒ 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)
