The cube of a number minus twice its square is equal to 80 times the number. If the number is greater than 0, what is the number?

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Accepted Answer

If the number is x, then the cube of the number is x 3 . Twice the square of the number is 2x 2 . The difference in those values is equal to 80 times the number (80x). Therefore, x 3 – 2x 2 = 80x. Move all terms onto one side of the equation, and factor the polynomial; x 3 – 2x 2 = 80x, x 3 – 2x 2 – 80x = 0; x 3 – 2x 2 – 80x = x(x 2 – 2x – 80) = x(x + 8)(x – 10). Set each factor equal to 0 to find the values of x that make the equation true. x = 0; x + 8 = 0, x = –8; x – 10 = 0, x = 10. The given situation is true for the numbers 0, –8, and 10, but only 10 is greater than 0.

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