x4-2x3-2x-1

Rearrange to get -1 just after x4

x4-1-2x3-2x

Group the first two terms in parentheses:

(x4-1)-2x3-2x

Take out common factor -2x from last two terms 
(Don't forget that when the -2x is divided by
-2x the quotient is +1 not -1)

(x4-1)-2x(x2+1)

Factor (x4-1) as the difference of two squares 

(In the US we do not say "factorise", we just say "factor",
just as we do not say "maths", we say "math".  Also we do 
not say "trapezium", we say "trapezoid"). :)

(x2-1)(x2+1)-2x(x2+1)

Take out common factor (x2+1)

(x2+1)[(x2-1)-2x]

Remove parentheses

(x2+1)[x2-1-2x]

Rearrange the terms in the brackets in descending
order of exponents, and change brackets to parentheses:

(x2+1)(x2-2x-1)

Edwin