A rectangular patio is 9 ft by 6 ft. When the length and width are increased by the same amount, the area becomes 88 sq ft. Ginger is using the zero product property to solve the equation open paren 6 plus x close paren times open paren 9 plus x close paren is equal to 88 What does the value of x in her solutions represent?

The equation (6 + x)(9 + x) = 88 uses x as the amount added to both the 6-ft width and the 9-ft length. Solving gives x² + 15x − 34 = 0, or (x + 17)(x − 2) = 0, so x = 2 or x = −17. These are two possible amounts of change; the negative value would make the dimensions invalid, but x still represents an amount by which both dimensions change. The correct choice is “two possible amounts by which the dimensions were changed.”

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