Question

Help with solving x^5 - 4x^4 - 2x^3 + 4x^2 + x= 0?

Answer 1

http://imgur.com/uSQm35n
Help would be greatly appreciated. :-)

Answer 2

First factor one x out of it.
So now you'd have: ( x )(x^4 - 4x^3 - 2x^2 + 4x + 1 )= 0
For the next step, you'll need to know how to do polynomial long division. Look up how to do it. It's easy. It's almost the same as regular long division.
We are just looking at the stuff in the second bracket now.
I use a bit of trial and error. Keep substituting in x=1 then try x = -1 and then x = 2, -2, ... into the part in the second brackets. You keep trying them until you get the equation to become zero. You'll find that x = -1 works.
(-1)^4 - 4(-1)^3 - 2(-1)^2 + 4(-1) + 1 = 1 - 4 - 2 + 1 = 0
So x = -1 leads to a root for the equation. x - (-1) = x + 1 is a factor of it.
Now use polynomial long division. I'll draw it.....

Answer 3

The 'Draw' function doesn't seem to be working for me today. I'll attach a file in a minute.

Answer 4

Let me know if you have any questions.

Answer 5

@jam333 - Thank SO much for showing me the work, but I had figured it out just a few seconds ago on my own! Nonetheless, I will give you credit and a medal for your effort. :-) Thanks again!

Answer 6

No problem.