We
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)

trapezoid

step-by-step explanation:

first i plotted all my points on a grid graph

i made sure all of them were in the correct quadrant

then i saw it was a trapezoid or a quadrilateral