Final answer:
To determine the expressions for the possible dimensions of the rectangular prism, we can substitute V = length x width x height in the given volume equation. Then factor out the common term 'm' to find the possible dimensions.
Step-by-step explanation:
To determine the expressions for the possible dimensions of the rectangular prism, we can use the given volume equation V = 15m + m² - 2m. We know that the volume of a rectangular prism is given by V = length x width x height. So we can replace V with length x width x height in the equation.
15m + m² - 2m = length x width x height
Now, we can factor out the common term 'm' from the equation:
m(15 + m - 2) = length x width x height.
Therefore, the possible dimensions of the rectangular prism are (15 + m - 2) for the length, m for the width, and m for the height.