Answer:
Step-by-step explanation:
Since this is a 4th degree polynomial, 2 of the roots will not be real. Finding them is next to impossible off a calculator until the real ones are found first. That's simple enough process.
[tex]5x^4-80=0[/tex] and
[tex]5x^4=80[/tex] Divide both sides by 5:
[tex]x^4=16[/tex] Rewrite to get
[tex](x^2)^2=(2^2)^2[/tex] which simplifies down to
[tex]x^2=4[/tex] Taking the square root of both sides gives you the real roots of x = 2 and -2.
That leaves you with 2 roots that are imaginary. After you factor out the 2 and the -2 by synthetic division, you are left with the depressed quadratic
[tex]5x^2+20=0[/tex] Factor out the 5:
[tex]5(x^2+4)[/tex]
So the final answer is D.
