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?

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