Final answer:
The cube of a number equals twenty-five times the number can be solved by the equation x^3 = 25x. After factoring, we find that both 5 and -5 satisfy this equation, so the correct answers are options A and B.
Step-by-step explanation:
The student is asking to solve an equation where the cube of a number equals twenty-five times the same number. This equation can be written as x3 = 25x. To find the number, we need to solve for x, which requires setting the equation to zero.
x3 - 25x = 0
We can factor x out of the equation:
x(x2 - 25) = 0
This simplifies down to:
x(x - 5)(x + 5) = 0
Therefore, x can be 0, 5, or -5. However, 0 is not an option in the given multiple choice answers, so we disregard it. Both 5 and -5 when cubed equal twenty-five times the same number. Thus, the numbers that satisfy the condition are 5 and -5, which correspond to options A and B respectively.