To find possible dimensions, we can factor the expression.
[tex][/tex]
[tex]V=6y^3+19y^2+10y[/tex]
[tex]V=y(6y^2+19y+10)[/tex]
[tex]V=y(6y^2+15y+4y+10)[/tex]
[tex]V=y(3y(2y+5)+2(2y+5))[/tex]
[tex]V=y((2y+5)(3y+2)[/tex]
So the possible dimensions of the rectangular prism are
{y, 2y+5, 3y+2}
