The volume of a rectangular prism is 6x3 + 25x2 + 21x − 10. The length of the prism is 2x + 5. The width of the prism is 3x − 1. What is an expression for the height of the prism?
Mathematics · Middle School · Thu Feb 04 2021
Answered on
Given :
Volume of rectangular prism = 6x³ + 25x² + 21x − 10
Length of prism = 2x + 5
Width of prism = 3x - 1
Height = ?
Formula :
Volume of rectangular prism = Length × Width × Height
6x³ + 25x² + 21x − 10 = (2x + 5) × (3x - 1) × Height
Height = 6x³ + 25x² + 21x − 10/(2x + 5) × (3x - 1)
Factoring the numerator, we get
Height = (x + 2)(2x + 5)(3x - 1)/(2x + 5)(3x-1)
Height = x + 2
Hence, Height of prism is x + 2