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Advanced Math / Nonlinear equations in one variable and systems of equations in two variables Difficulty: Medium

open parenthesis, x minus 4, close parenthesis, times, open parenthesis, x plus 2, close parenthesis, times, open parenthesis, x minus 1, close parenthesis, equals 0

What is the product of the solutions to the given equation?

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Explanation

Choice D is correct. By the zero-product property, if open parenthesis, x minus 4, close parenthesis, times, open parenthesis, x plus 2, close parenthesis, times, open parenthesis, x minus 1, close parenthesis, equals 0, then x minus 4, equals 0, x plus 2, equals 0, or x minus 1, equals 0. Solving each of these equations for x yields x equals 4, x equals negative 2, or x equals 1. The product of these solutions is 4 times negative 2, times 1, equals negative 8.

Choice A is incorrect and may result from sign errors made when solving the given equation. Choice B is incorrect and may result from finding the sum, not the product, of the solutions. Choice C is incorrect and may result from finding the sum, not the product, of the solutions in addition to making sign errors when solving the given equation.