What are the roots of the polynomial equation x cubed minus 10 x is equal to negative 3 x squared plus 24 ? Use a graphing calculator and a system of equations.

Graph the two sides as y = x³ − 10x and y = −3x² + 24; their intersection x-values satisfy the equation. Rearranging gives x³ + 3x² − 10x − 24 = 0, which factors as (x − 3)(x + 2)(x + 4) = 0. Thus the roots are −4, −2, and 3, which is choice B.

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