Help with this polynomial equation problem please - due @ 12am?

Question

Yes I need help on homework...this is easy college algebra stuff but I can't seem to remember it from high school. I actually didn't procrastinate, I've been working on it all afternoon - help is appreciated! Thanks!
Help me solve the polynomial equation!?
2x5 + 2x4 - 6x3 - 6x2 - 8x - 8 = 0

How do I go about this?

Solve the polynomial equation.
2x^5 + 2x^4 -6x^3-6x^2 -8x - 8 = 0.

I've tried factoring, synthetic division, etc. All I've come up with is that x = -1 is one possibility. These are my options:
a) x = 1, -2, -1, +-i
b) x = 2, -1
c) x = -2, -1, i
d) x = -2, 2, 1, +-i

Answer 1

Try to solve it by factor by grouping.

2x^4(x + 1) - 6x^2(x + 1) - 8(x +1) = 0

(x+1)^3(2x^4 - 6x^2 - 8) = 0

(x+1)^3 (2)(x^4 - 3x^2 - 4) = 0

(x+1)^3 (2) (x^2 + 1) (x^2 - 4) = 0

so set all of the factors equal to zero.
(x+1)^3 = 0 so x = -1
(x^2 + 1) = 0 so x = positive or negative i
(x^2 - 4) = 0 so x = positive or negative 2

So i would go with answer choice c.

Answer 2

x^3 - 4x^2 - 12x + 35= 0 This equation is not factorable so the best method is to try and find roots that almost satisfy the equation. If you try a few numbers you will see that roots are located at approximately -3, 2, and 5 So use Newton's method to isolate the roots to the accuracy desired. Find out where f(x) changes sign and then Newton's method will give you a smaller range where the zero occurs and you can continue getting new estimates. For example the root that is somwhere around 2 is actually at between 2.1921 and 2.1926. So you culd say that the root si 2.192 to 3 significant digits. If you do not know Newton's method look it up on the Internet.

Answer 3

try this
10+8-18-12-8x-8=0 add 10 to the 8
18-18-12-8x-8=0 add the 18 to the -18
-12-8x-8=0 add 12 to both sides
-8x-8=12 add 8 to both sides
-8x=20 divide both sides by -8
x= -2.5