Expression for the height of the prism is x + 2
Solution:
Given that,
[tex]Volume\ of\ a\ rectangular\ prism = 6x^3+25x^2 + 21x - 10[/tex]
[tex]Length\ of\ prism = 2x + 5[/tex]
[tex]Width\ of\ prism = 3x-1[/tex]
To find: height of prism
The volume of rectangular prism is given by formula:
[tex]Volume = length \times width \times height[/tex]
Solving for height we get,
[tex]height = \frac{volume}{length \times width}[/tex]
Substituting the values we get,
[tex]height = \frac{6x^3+25x^2+21x-10}{(2x+5)(3x-1)}[/tex]
Factor the numerator
[tex]height = \frac{(x+2)(3x-1)(2x+5)}{(2x+5)(3x-1)}[/tex]
Cancel the common factors,
[tex]height = x + 2[/tex]
Thus expression for the height of the prism is x + 2
