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!
To determine which model represents the rectangular prism with a volume of 6x^3 - x^2 - 2x, we need to match the terms of the volume expression with the corresponding dimensions of the rectangular prism.
The volume of a rectangular prism is given by the formula V = length * width * height.
Comparing the expressions, we have:
V = 6x^3 - x^2 - 2x
Length = ?
Width = ?
Height = ?
To factorize the volume expression, we can look for common factors. In this case, there are no common factors to factorize out. So, we need to find three binomial factors that multiply together to give the given volume expression.
By comparing with the answer choices, we can consider the options one by one:
A. Height: 3x - 2
Length: 2x + 1
Width: x
If we multiply the dimensions together, we get:
(3x - 2) * (2x + 1) * (x) = 6x^3 - 3x^2 + 2x^2 - x = 6x^3 - x^2 - x
So, this model does not represent the given volume expression.
B. 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 + 4x^2 - 2x = 6x^3 + 3x^2 - 2x
So, this model does not represent the given volume expression.
C. Height: 3x - 2
Length: 2x - 1
Width: x
If we multiply the dimensions together, we get:
(3x - 2) * (2x - 1) * (x) = 6x^3 - 3x^2 - 4x^2 + 2x = 6x^3 - x^2 - 2x
So, this model represents the given volume expression.
D. Height: 2x - 2
Length: 3x + 1
Width: x
If we multiply the dimensions together, we get:
(2x - 2) * (3x + 1) * (x) = 6x^3 - 2x^2 + 3x^2 - x = 6x^3 + x^2 - x
So, this model does not represent the given volume expression.
Therefore, the correct model that represents the rectangular prism with a volume of 6x^3 - x^2 - 2x is option C. Height: 3x - 2, Length: 2x - 1, Width: x.
To find the correct model that represents the rectangular prism with a volume of 6x^3 -x^2 -2x, we need to compare the equation of the volume with the formulas for the volume of a rectangular prism.
The formula for the volume of a rectangular prism is given by V = l * w * h, where l is the length, w is the width, and h is the height.
Comparing the given equation 6x^3 - x^2 - 2x with the formula V = l * w * h, we can equate the coefficients of the variables.
From the given options:
A. Height: 3x-2 Length: 2x+1 Width: x
The volume would be (2x + 1) * x * (3x - 2) = 6x^3 - 3x^2 - 4x + 2, which is not equal to the given equation.
B. Height: 3x+2 Length: 2x-1 Width: x
The volume would be (2x - 1) * x * (3x + 2) = 6x^3 + x^2 - 2x - 1, which is not equal to the given equation.
C. Height: 3x-2 Length: 2x-1 Width: x
The volume would be (2x - 1) * x * (3x - 2) = 6x^3 - x^2 - 4x + 2, which is not equal to the given equation.
D. Height: 2x-2 Length: 3x+1 Width: x
The volume would be (3x + 1) * x * (2x - 2) = 6x^3 - x^2 - 4x + 2, which is equal to the given equation.
Therefore, the correct model that represents the rectangular prism is option D. Height: 2x-2 Length: 3x+1 Width: x.
since V = length(width)(height)
6x^3 - x^2 - 2x must be the product of 3 factors.
the first one is obvious, a common factor of x
= x(6x^2 - x - 2)
and the quadratiac factors to ((2x+1)(3x-2)
so which one fits ?