Four times the cube of a number is equal to 48 times the number minus four times the square of the number. If the number is greater than 0, what is the number?

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If the number is x, then four times the cube of the number is 4x 3 . That value is equal to 48 times the number (48x) minus four times the square of the number (4y 2 ). Therefore, 4x 3 = 48x – 4x 2 . Move all terms onto one side of the equation, and factor the polynomial; 4x 3 = 48x – 4x 2 , 4x 3 + 4x 2 – 48x = 0; 4x 3 + 4x 2 – 48x = 4x(x 2 + x – 12) = 4x(x + 4)(x – 3). Set each factor equal to 0 to find the values of x that make the equation true. 4x = 0, x = 0; x + 4 = 0, x = –4; x – 3 = 0, x = 3. The given situation is true for the numbers 0, –4, and 3, but only 3 is greater than 0.

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