Problem

Compare \(x+2\) as a polynomial factor with the shared factor in \([(x+2)(x-1)]/(x+2)\). Account for \(x=-2\) in each expression and identify the resulting graph features.

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Polynomial x+2: x=-2 is allowed and gives intercept (-2,0). Rational shared factor: x=-2 cancels but remains excluded, so the reduced line y=x-1 has a hole at (-2,-3).

Polynomial x+2: x=-2 is allowed and gives intercept (-2,0). Rational shared factor: cancellation restores x=-2, so the reduced line includes the point (-2,-3).

Polynomial x+2: x=-2 is excluded and creates a hole. Rational shared factor: x=-2 cancels and is included as point (-2,-3).

Polynomial x+2: x=-2 is allowed and gives intercept (-2,0). Rational shared factor: x=-2 cancels but creates a vertical asymptote at x=-2.

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Compare \(x+2\) as a polynomial factor with the shared factor in \([(x+2)(x-1)]/(x+2)\). Account for \(x=-2\) in each expression and identify the resulting graph features.

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