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A rectangular prism has a square base with edge length (x+1). Its volume is (x+1)²(x-3). What does the expression (x+1)(x-3) represent?

(A) area of the base
(B) area of one side
(C) height of the prism
(D) surface area of the prism

1 Answer

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Final answer:

The expression (x+1)(x-3) represents the height of the prism. The volume of a rectangular prism is calculated as the product of the area of the base and the height, and since the base is a square, (x+1)² is its area and (x-3) is the height.

Step-by-step explanation:

We are given that a rectangular prism has a square base with edge length (x+1) and its volume is given by (x+1)²(x-3). In geometry, the volume of a rectangular prism is found by multiplying the area of the base (A) by the height (h) of the prism, indicated by the formula V = Ah. Thus, the expression (x+1)² represents the area of the square base of the prism, since the base is a square and the area of a square is the square of its side length.

Therefore, the remaining factor in the volume expression, (x-3), represents the height of the prism. To see this, we recognize that the volume formula can be rearranged as Volume = Base Area × Height, which aligns with the given expression for the volume of the prism. Thus, the expression (x+1)(x-3) represents the height of the prism (Option C).

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