prove that x^6-x^5-x^4-x^3-x^2-x+1>0 is true for any number

Question

Please someone explain to me this, I couldn't understand the teacher when they talked about something similar to this and I didn't get it...

Answer 1

not even true,
e.g. let x = 1
x^6-x^5-x^4-x^3-x^2-x+1>0
1 - 1 - 1 - 1 - 1 - 1 - 1 + 1 > 0 is false

all I needed was ONE exception and the statement is false.

see:
http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E6-x%5E5-x%5E4-x%5E3-x%5E2-x%2B1