x^3+x^2-x-1

Question

How to factor x^3+x^2-x-1

Answer 1

x^3 + x^2 - x - 1

 

Factor x^2 from the first two terms:

 

x^2(x + 1) - x - 1

 

Factor a -1 from the last two terms:

 

x^2(x+1) - 1(x+1)

 

Simplify:

 

(x^2 - 1)(x+1)

 

 Since the first binomial is the difference of two squares:

 

(x+1)(x-1) (x+1)

 

Combine:

 

(x+1)^2 (x-1)   or (x-1) (x+1)^2

 

 

 

Alternatively:

 

Regroup the terms to the following:

(x^3 - x) + (x^2 - 1)

 

Factor out x from the first two terms:

x(x^2 - 1) + 1(x^2 - 1)

 

(x+1)(x^2 - 1)

 

(x+1)(x+1)(x-1)

 

(x + 1)^2 (x-1) or (x-1)(x+1)^2

 

First binomial is a difference of two squares, so factor:

 

(x+1)(x-1)(x+1)

 

Combine:

 

(x-1)(x+1)^2