Answer
$2x^3+12x^2+12x+10$
Work Step by Step
Step 1. The volume of the solid part can be taken as the difference between the entire rectangular prism and the volume of the slot.
Step 2. The dimensions for the entire prism can be found as $x+5, 2x+1, x+2$
Step 3. The dimensions for the slot can be found as $x+5, x, 3$
Step 4. The volume of the solid is then $V=(x+5)(2x+1)(x+2)-3x(x+5)=(x+5)(2x^2+4x+x+2-3x)=(x+5)(2x^2+2x+2)=2(x+5)(x^2+x+1)=2(x^3+x^2+x+5x^2+5x+5)=2(x^3+6x^2+6x+5)=2x^3+12x^2+12x+10$
