(X^3 + 2x^2-x-2)/(x+2)=?

Mathematics

2 answers:

RideAnS [48]2 years ago

7 0

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