Respuesta :
Answer: 2x(x^2-2)(x+1)
=========================================================
Explanation:
First factor out the GCF 2x
2x^4+2x^3-4x^2-4x
2x*x^3+2x*x^2-2x*2x-2x*2
2x(x^3 + x^2 - 2x - 2)
Then let's factor the expression inside the parenthesis using the factor by grouping method
x^3 + x^2 - 2x - 2
(x^3 + x^2) + (- 2x - 2)
x^2(x + 1) - 2(x + 1)
(x^2 - 2)(x+1)
We see that x^3 + x^2 - 2x - 2 factors to (x^2-2)(x+1)
Overall, the original expression fully factors to 2x(x^2-2)(x+1)
length = 2x
width = x^2-2
height = x+1
The order of length, width, and height doesn't matter.
The volume as the product its dimensions 2x*( x²-2)*(x+1).
What is Volume?
Volume is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.
Given:
volume of a rectangular prism is given by the expression 2x^4+2x³-4x²-4x
=2x*x^3+2x*x^2-2x*2x-2x*2
=2x(x³ + x² - 2x - 2)
Now, we get the factor 2x(x³ + x² - 2x - 2).
Keeping aside 2x we will now focus on (x³ + x² - 2x - 2)
We already get the one factor 2x and now using (x³ + x² - 2x - 2) to get the other two factors.
Now solving x³ + x² - 2x - 2
=(x³ + x²) + (- 2x - 2)
= x²(x + 1) - 2(x + 1)
=( x² - 2)(x+1)
Now we get the two factors ( x² - 2)(x+1).
The expression for volume as the product its dimensions is 2x*( x²-2)*(x+1)
Hence, volume as the product its dimensions is 2x*( x²-2)*(x+1).
Learn more about Volume here:
https://brainly.com/question/13338592
#SPJ2
