The volume of a right rectangular prism is expressed by V(x) = x^3+2x^2-x-2. What could the dimensions of the prism be?

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Answer 1 · 2015-07-11T17:41:35

#V(x) = x^3+2x^2-x-2 = (x-1)(x+1)(x+2)#

So the dimensions could be #(x-1) xx (x+1) xx (x+2)#

Factor by grouping

#V(x) = x^3+2x^2-x-2#

#= (x^3+2x^2)-(x+2)#

#= x^2*(x+2)-1*(x+2)#

#= (x^2-1)(x+2)#

#= (x^2-1^2)(x+2)#

#= (x-1)(x+1)(x+2)#

...using the difference of squares identity:

#a^2-b^2 = (a-b)(a+b)#