Question

a rectangular prism has a volume x^3 + 5x^2 + 6x, what expressions can represent the dimensions of the rectangular prism

Answer 1

V = x^3 + 5x^2 + 6x = x * ( x^2 + 5x + 6 ) ;
But, x^2 + 5x + 6 = x^2 + 2x + 3x + 6 = x( x+ 2 ) + 3( x + 2 ) = ( x + 2 )( x + 3 ) ;
Then, V = x^3 + 5x^2 + 6x = x( x + 2 )( x + 3 ); 
Rectangular prism  has three dimensions:  width,  height and  base (or length);
V = w * b * h ;
Finally, x, x + 2 and x + 3 represent the dimensions of the rectangular prism.