Answer:
(x-1)(x+1)(x+2)
Step-by-step explanation:
Lets use grouping method to factor
[tex]x^3+2x^2-x-2[/tex]
We group first two terms and last two terms
[tex](x^3+2x^2)+(-x-2)[/tex]
Factor out GCf from each group
GCf for first group is x^2 and for second group is -1
[tex]x^2(x+2)-1(x+2)[/tex]
We have x+2 in common , so we factor out x+2
[tex](x^2-1) (x+2)[/tex]
Now we factor x^2 -1
We use difference of squares formula a^2-b^2 = (a+b)(a-b)
x^2 -1 can be written as x^2 - 1^2
[tex]x^2 - 1^2 = (x+1)(x-1)[/tex]
So factors are (x+1)(x-1)(x+2)
We write it in increasing order
(x-1)(x+1)(x+2)
