What are the roots of the polynomial equation x cubed minus 7 x is equal to 6 x minus 12 ? Use a graphing calculator and a system of equations.

Set the two expressions equal and move everything to one side: x³ − 7x = 6x − 12 becomes x³ − 13x + 12 = 0. Factoring gives (x − 1)(x − 3)(x + 4) = 0, so the roots are 1, 3, and −4. These are the x-coordinates where the graphs y = x³ − 7x and y = 6x − 12 intersect, matching choice A: negative 4, 1, 3.

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