# How do you factor #x³+x²-x-1#?

##### 2 Answers

The complete factorization is

#### Explanation:

I used synthetic division to solve this. (Do you need further explanation?)

You can factor by grouping to find:

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

Then use the difference of squares identity to find:

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

#### Explanation:

First factor by grouping:

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

Then notice that

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

Alternatively, notice that the sum of the coefficients (

Divide

Then recognise that