Question 818314
{{{3x^3 + 9x^2 + 6x=3x(x^2+3x+2)=3x(x+1)(x+2)}}}
So {{{3x^3 + 9x^2 + 6x}}} can be written as the 3-factor product
{{{(3x)*(x+1)*(x+2)}}}
Maybe the prism your teacher had in mind
(or the prism that the textbook writer had in mind)
has for dimensions
{{{3x}}} , {{{x+1}}} and {{{x+2}}} .
That would be my bet.
 
However, why not have a prism with dimensions given by
{{{x}}} , {{{3x+3=3(x+1)}}} , and {{{x+2}}} ,
or maybe
{{{x}}} , {{{x+1}}} , and {{{3x+6=3(x+2)}}} ,
or maybe
{{{sqrt(3)x}}} , {{{sqrt(3)x+sqrt(3)}}} , and {{{x+2}}} ,
or maybe
{{{x}}}, {{{x+1}}} , and {{{0.5x+1}}} .
The possibilities are endless.
How limited are the imaginations of the teacher and the textbook writer?