how to factor x^3+x^2-x-1?

How to factor x^3+x^2-x-1?

Factor by grouping...

(x³ + x²) - (x + 1) = x²(x + 1) - (x + 1) = (x + 1)(x² - 1)

factor the DIFFERENCE OF SQUARES...

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

check by multiplying...do something !

EDIT: thumbs down for the correct answer...UP YOURS !

for this problem, you can factor by grouping:
(x^3+x^2) (-x-1)
Take out x^2 from first parenthesis leaving you with x^2(x+1)
Take out a -1 from the second parenthesis leaving you with -1(x+1)
Combine to result in (x^2-1) (x+1)
Factor the first parenthesis using difference of squares resulting in (x-1)(x+1)
The final answer is (x-1)(x+1)(x+1) or (x+1)^2 (x-1)

You split the two terms.

x^3 + x^2. Now take the greatest common factor, x^2. Now you have x^2 (x+1)

Then, take -1 out of -x-1. Then you have the factors (x^2-1) (x+1).

Your roots are 1, 1, and -1.

x²(x+1)-(x+1) = (x+1)(x²-1) = (x+1)(x+1)(x-1) = (x+1)²(x-1) <== ans.

The solution of this question x^3 + x^2 - x - 1
= x^2(x + 1) - (x + 1)
= (x^2 - 1)(x + 1)
= (x + 1)^2(x - 1)

ans.=(x+1)^2,(x-1)
checking:
=(x+1)(x+1)
=x^2+2x+1
=(x^2+2x+1)(x-1)
=x^3+x^2-x-1

x^3+x^2-x-1=0
x^2(x+1)-1(x+1)=0
(x^2-1)(x+1)=0
x^2=1,x=-1
x=1,x=-1(twice)

The easiest way to factor any polynomial is to look for patterns and group terms. In this case I can see the expression x^3+x^2-x-1 is easy to factor.

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

x^2 - 1 is the difference of two squares which means (x^2-1) = (x+1)(x-1)
We know this because x^2-1 = x^2 + x- x- 1 = x(x+1) - (x+1) = (x+1)(x-1) (x - x = 0)

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

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

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

You could factor an x2 out of the first two terms and a -1 out of the second two terms:
x2(x + 1)-1(x + 1)

You can then factor out the (x + 1) out of both terms:
(x2 -1)(x + 1)

Then notice that (x2 - 1) is a difference of squares factorable into (x -1)(x + 1)
So your final answer should be (x - 1)(x + 1)( x + 1)

Hint: Divide by (x-1)