# Divide (a^3+a^2-4a-4)/(a-2)

a3+a2-4a-4a-2
Simplify the numerator.
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(a3+a2)-4a-4a-2
Factor out the greatest common factor (GCF) from each group.
a2(a+1)-4(a+1)a-2
a2(a+1)-4(a+1)a-2
Factor the polynomial by factoring out the greatest common factor, a+1.
(a+1)(a2-4)a-2
Rewrite 4 as 22.
(a+1)(a2-22)a-2
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=a and b=2.
(a+1)(a+2)(a-2)a-2
(a+1)(a+2)(a-2)a-2
Cancel the common factor of a-2.
Cancel the common factor.
(a+1)(a+2)(a-2)a-2
Divide (a+1)(a+2) by 1.
(a+1)(a+2)
(a+1)(a+2)
Expand (a+1)(a+2) using the FOIL Method.
Apply the distributive property.
a(a+2)+1(a+2)
Apply the distributive property.
a⋅a+a⋅2+1(a+2)
Apply the distributive property.
a⋅a+a⋅2+1a+1⋅2
a⋅a+a⋅2+1a+1⋅2
Simplify and combine like terms.
Simplify each term.
Multiply a by a.
a2+a⋅2+1a+1⋅2
Move 2 to the left of a.
a2+2⋅a+1a+1⋅2
Multiply a by 1.
a2+2a+a+1⋅2
Multiply 2 by 1.
a2+2a+a+2
a2+2a+a+2