Question 823886
<pre>x<sup>4</sup>-2x<sup>3</sup>-2x-1

Rearrange to get -1 just after x<sup>4</sup>

x<sup>4</sup>-1-2x<sup>3</sup>-2x

Group the first two terms in parentheses:

(x<sup>4</sup>-1)-2x<sup>3</sup>-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)

(x<sup>4</sup>-1)-2x(x<sup>2</sup>+1)

Factor (x<sup>4</sup>-1) as the difference of two squares 

<font size = 1>(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"). :)</font>

(x<sup>2</sup>-1)(x<sup>2</sup>+1)-2x(x<sup>2</sup>+1)

Take out common factor (x<sup>2</sup>+1)

(x<sup>2</sup>+1)[(x<sup>2</sup>-1)-2x]

Remove parentheses

(x<sup>2</sup>+1)[x<sup>2</sup>-1-2x]

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

(x<sup>2</sup>+1)(x<sup>2</sup>-2x-1)

Edwin</pre>