The volume of a box is x^3 + 4x^2 +4x. Explain how you know the box is not a cube.

Question

hartnn · Answer

whats the formula of volume of a cube ? you know ?

gorv · Answer

find root of equation if all roots are coming equal than it will be cube

gorv · Answer

x(x^2+4x+4)
factorise further

anonymous · Answer

So you took out from the parenthesis thats why its x?

anonymous · Answer

How can I factorize further on?

hartnn · Answer

x^2+4x+4 is a simple quadratic to factorize, can you try ?
2 numbers with sum =4 and product = 4 are ??

anonymous · Answer

x(x+4+4)

hartnn · Answer

for factorizing the standard quadratic expression,$ ax^2+bx+c$, we need 2 numbers whose sum is 'b' and product = ac

For example, in x^2 + 6x+9, 
2 numbers with sum = 6 and product =9 are 3,3 

for your Question, 
can you find 2 numbers whose sum = 4 and product = 4 ?

anonymous · Answer

ohhh

anonymous · Answer

2

anonymous · Answer

How do I know if it is a cube then?

hartnn · Answer

it would be a cube if ALL 3 factors are SAME
(because volume of a cube with side x is x*x*x)

anonymous · Answer

So its not cause. 3,4,4 ?

hartnn · Answer

we got one factor as x
we need to find other 2

kainui · Answer

What is x? If x doesn't have any kind of units associated with it, I don't really see any reason to believe that this isn't the volume of a cube. Just take the cube root of that equation and you have the equation for one of the side lengths for a cube with that volume.