Question

The area of a rectangle is given by the function A(x) = 2x3 + 4x2 + 3x + 6. If the length is defined by x + 2, what is the width of the rectangle?

Answer 1

`2x^2\text{ + 3 (option A)}`

Step-by-step explanation:
`\begin{gathered} \text{Area of the rectangle = }A(x) \\ A(x)=2x^3+4x^2+3x+6 \\ \text{length of the rectangle = x + 2} \\ \text{width of the rectangle = ?} \\ \\ \end{gathered}`
`\begin{gathered} \text{Area of rectangle = length }*\text{ width} \\ \text{width = }\frac{Area\text{ of rectangle}}{\text{length}} \\ \text{width = }\frac{2x^3+4x^2+3x+6}{x\text{ + 2}} \end{gathered}`

Applying long division:

`\begin{gathered} \frac{2x^3+4x^2+3x+6}{x\text{ + 2}}\text{ = }2x^2\text{ + 3} \\ \text{width = }2x^2\text{ + 3 (option A)} \end{gathered}`