A rectangular flower garden is 4 feet longer than its width w. Write a polynomial that represents the area of the garden. Write your answer in simplified form.
a = w(w+4)
. . .
To find the polynomial that represents the area of the rectangular flower garden, we need to understand the relationship between the length, width, and area.
Let's start by assigning a variable to represent the width of the garden. In this case, let's use "w" as the width.
According to the problem, the garden is 4 feet longer than its width. Therefore, the length of the garden can be expressed as "w + 4".
The area of a rectangle can be calculated by multiplying its length and width. So, the area of the garden is given by:
Area = Length × Width
Substituting "w + 4" for the length and "w" for the width, we get:
Area = (w + 4) × w
To simplify this expression, we can distribute the w on the left side:
Area = w² + 4w
Therefore, the polynomial that represents the area of the rectangular flower garden is:
A(w) = w² + 4w