Question

The volume of water in a rectangular swimming pool can be modeled by the polynomial 2x^3-9x^2+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?

Answer 1

The area of the base is given by

`B=(V)/(h)`

We are given

`V=2x^(3)-9x^(2)+7x+6` and
`h=2x+1`

`\rightarrow B=(2x^(3)-9x^(2)+7x+6)/(2x+1)`
which we can solve with long division:
x^2 -5x+6
2x+1 | 2x^3-9x^2+7x+6
2x^3+ x^2
--------------------------
-10x^2+7x
-10x^2-5x
--------------------
12x+6
12x+6
-----------
0

So
`B=x^(2)-5x+6`
which can be factored as

`(x-2)(x-3)`

So the length and width are
`x-2` and
`x-3`.