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

Question

asked Nov 19, 2022 165k views

1 Answer

Reb · Answer 1 · 2022-11-25T06:18:17+0000

Answer:

$(A)\:x^(2) -1$

Explanation:

(x^(3) +2x^(2) -x-2)/(x+2

Factor expressions that haven't been factored yet.

$\longmapsto$
((x-1)(x+1)(x+2))/(x+2)

Cancel out x+2 in both numerator and denominator.

$\longmapsto$
(x-1)(x+1)

Apply Difference of Two Squares Formula:
$\left(a+b\right)\left(a-b\right)=a^2-b^2$

$\longmapsto$
$\left(x+1\right)\left(x-1\right)=x^2-1^2$

$\longmapsto$
1^2=1

$\longmapsto$
x^2-1

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