[tex]2x^2\text{ + 3 (option A)}[/tex]
Explanation:[tex]\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}[/tex][tex]\begin{gathered} \text{Area of rectangle = length }\times\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}[/tex]
Applying long division:
[tex]\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}[/tex]
