Question

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

Answer 1

`(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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