Answer:
[tex]x + 3 + \dfrac{2}{5x}[/tex]
Step-by-step explanation:
The area of the base of a cylinder is found by dividing the volume of the cylinder by its height:
[tex]\boxed{\textsf{Area of the base of cylinder}=\dfrac{\textsf{Volume}}{\textsf{Height}}}[/tex]
In this case:
- Volume = 5x² + 15x + 2
- Height = 5x
Therefore, to find the expression that represents the area of the base of the cylinder, we need to divide the expression for the volume by the expression for the height using long division:
[tex]\large \begin{array}{r}x+3\phantom{)}\\5x{\overline{\smash{\big)}\,5x^2 + 15x + 2\phantom{)}}\\{-~\phantom{(}\underline{(5x^2)\phantom{-wwpppl)}}\\15x + 2\phantom{)}\\-~\phantom{()}\underline{(15x)\phantom{bwb}}\\2\phantom{)}\\\end{array}[/tex]
So, the quotient of the division is x + 3 and the remainder is 2.
The solution is the quotient plus the remainder divided by the divisor.
Therefore, the expression that represents the area of the base of the cylinder is:
[tex]\Large\boxed{\boxed{x + 3 + \dfrac{2}{5x}}}[/tex]
