QuestionDecember 14, 2025

Serenity uses the following polynomial expression x(x+5)(x-7) to model the volume of a rectangular prism.The height is shorter than the width and the length. What is the height of this prism? A. x ) B. x-7 C. x+5 D. x^3-2x^2-35x

Serenity uses the following polynomial expression x(x+5)(x-7) to model the volume of a rectangular prism.The height is shorter than the width and the length. What is the height of this prism? A. x ) B. x-7 C. x+5 D. x^3-2x^2-35x
Serenity uses the following polynomial expression x(x+5)(x-7) to model the volume of a rectangular prism.The height is
shorter than the width and the length. What is the height of this prism?
A. x
) B. x-7
C. x+5
D. x^3-2x^2-35x

Solution
4.6(205 votes)

Answer

B. x-7 Explanation 1. Identify polynomial factors as dimensions The expression x(x+5)(x-7) represents the product of three dimensions: x, x+5, and x-7. 2. Compare dimension sizes Since x 7. 3. Match with answer choices The height (shortest) is x-7.

Explanation

1. Identify polynomial factors as dimensions<br /> The expression $x(x+5)(x-7)$ represents the product of three dimensions: $x$, $x+5$, and $x-7$.<br />2. Compare dimension sizes<br /> Since $x < x+5$ and $x < x-7$ only if $x < -7$, but for positive $x$, $x-7 < x < x+5$. Thus, $x-7$ is the shortest when $x > 7$.<br />3. Match with answer choices<br /> The height (shortest) is $x-7$.
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