Final Answer:
The correct expression for the area of the base of the rectangular prism is c) 3x² + 2x - 9.
Step-by-step explanation:
The volume of a rectangular prism is given by the product of its base area and its height. The expression provided, 12x³ - 23x² + 46x - 45, represents the volume of the base. To find the area of the base, we divide the volume by the height of the rectangular prism, which is 4x + 5.
Applying polynomial division, (12x³ - 23x² + 46x - 45) ÷ (4x + 5), we get the quotient as 3x² + 2x - 9, representing the area of the base of the rectangular prism. This quotient is derived by dividing the volume expression by the height expression.
Therefore, the correct expression for the area of the base of the rectangular prism is 3x² + 2x - 9, obtained by dividing the given volume expression by the height of the prism. This explanation demonstrates the process of obtaining the area expression by dividing the volume expression by the height of the rectangular prism. OPTION C