Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(x^3+2x^2)−x−2
—————————
x+2
Factor out the greatest common factor (GCF) from each group.
x^2(x+2)−(x+2)
————————-
x+2
Factor the polynomial by factoring out the greatest common factor, x+2
(x+2)(x^2−1)
———————
x+2
Rewrite 1 as 1^2
(x+2)(x^2−1^2)
————————
x+2
Since both terms are perfect squares, factor using the difference of squares formula, a^2−b^2=(a+b)(a−b) where a=x and b=1 .
(x+2)(x+1)(x−1)
————————
x+2
Cancel the common factor of x+2 .
Divide (x+1)(x−1) by 1.
(x+1)(x−1)
Expand (x+1)(x−1) using the FOIL Method.
Apply the distributive property.
x(x−1)+1(x−1)
Apply the distributive property.
x⋅x+x⋅−1+1(x−1)
Apply the distributive property.
x⋅x+x⋅−1+1x+1⋅−1
Simplify and combine like terms.
Simplify each term.
x^2−x+x−1
Add−x and x .
x^2+0−1
Add x^2 and 0.
x^2−1
