The volume of a rectangular prism is 6x^3 -x^2 -2x. Which model could represent the rectangular prism?
A. Height: 3x-2 Length: 2x+1 Width: x
B. Height: 3x+2 Length: 2x-1 Width: x
C. Height: 3x-2 Length: 2x-1 Width: x
D. Height: 2x-2 Length: 3x+1 Width: x
I don't understand how to do the problem, I would appreciate if someone could explain the steps. Thank you!
I think I may have put this in the wrong subject last time. Sorry for the repeated question.
factor:6x^3 -x^2 -2x
x(6x^2-x-2)
x(2x+1)(3x-2)
so since volume=L*W*h those three factors are it.
To determine which model represents the rectangular prism with a given volume, we need to compare the equation of the volume to the dimensions given in each option.
The volume of a rectangular prism is calculated by multiplying its length, width, and height. In this case, the volume equation is given as 6x^3 - x^2 - 2x.
Let's analyze each option:
Option A:
Height: 3x - 2
Length: 2x + 1
Width: x
If we multiply the dimensions together, we get:
(3x - 2) * (2x + 1) * x = 6x^3 - x^2 + 3x - 2x - 2 = 6x^3 - x^2 + x - 2
This does not match the given volume equation, so Option A can be eliminated.
Option B:
Height: 3x + 2
Length: 2x - 1
Width: x
Multiplying the dimensions, we have:
(3x + 2) * (2x - 1) * x = 6x^3 + x^2 - 3x - 2x^2 + 2x - x = 6x^3 - x^2 - 2x
This matches the given volume equation, so Option B could represent the rectangular prism.
Option C:
Height: 3x - 2
Length: 2x - 1
Width: x
Multiplying the dimensions, we get:
(3x - 2) * (2x - 1) * x = 6x^3 - x^2 - 3x + 2x - 2 = 6x^3 - x^2 - x - 2
This does not match the given volume equation, so Option C can be eliminated.
Option D:
Height: 2x - 2
Length: 3x + 1
Width: x
Multiplying the dimensions, we have:
(2x - 2) * (3x + 1) * x = 6x^3 + 2x^2 - 6x - 2x + 2 = 6x^3 + 2x^2 - 8x + 2
This does not match the given volume equation, so Option D can be eliminated.
Therefore, the model that represents the rectangular prism with the given volume is Option B:
Height: 3x + 2
Length: 2x - 1
Width: x