Question

Ok so this is so confusing The volume of water in a rectangular swimming pool can be modeled by the polynomial 2x3 _ 9x2 + 7x + 6. If the depth of the pool is given by the polynomial 2x + 1, what polynomials express the length and width of the pool? Why couldn't they just give me the volume?

Answer 1

The volume formula is V= l x L x H, l=width, L=Length, H= Depth, so 
2x3 _ 9x2 + 7x + 6 = l x L x (2x + 1), because H=(2x + 1), so 
l x L= (2x3 _ 9x2 + 7x + 6 )/ (2x + 1) = (2x3 _ 9x2 + 7x + 6 ) X [1/(2x + 1)]
case1: l= (2x3 _ 9x2 + 7x + 6 ) or L= 1/(2x + 1), case2: L= (2x3 _ 9x2 + 7x + 6 ) or l= 1/(2x + 1)
the why question:
perhaps there is similarity of value between volume and l, or volume and L