Question

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

Answer 1

Answer:

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

Step-by-step explanation:

$(x^{3} +2x^{2} -x-2)\div(x+2$

Factor expressions that haven't been factored yet.

$\longmapsto$ $\frac{(x-1)(x+1)(x+2)}{x+2}$

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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