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?
The area of the base is given by [tex]B=\frac{V}{h}[/tex]
We are given [tex]V=2x^{3}-9x^{2}+7x+6[/tex] and [tex]h=2x+1[/tex] [tex]\rightarrow B=\frac{2x^{3}-9x^{2}+7x+6}{2x+1}[/tex] 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 [tex]B=x^{2}-5x+6[/tex] which can be factored as [tex](x-2)(x-3)[/tex]
So the length and width are [tex]x-2[/tex] and [tex]x-3[/tex].
