Answer :
Given:
The length of a rectangle is 5 centimeters less than 2 times the width.
To find:
The polynomial expression that represents the area of the rectangle, then simplify the expression.
Solution:
Let [tex]x[/tex] be the width of the rectangle.
The length of a rectangle is 5 centimeters less than 2 times the width.
2 times the width = [tex]2x[/tex]
5 centimeters less than 2 times the width = [tex]2x-5[/tex]
Length of the rectangle = [tex]2x-5[/tex]
We know that, the area of a rectangle is:
[tex]A=length \times width[/tex]
[tex]A=(2x-5)\times x[/tex]
[tex]A=2x^2-5x[/tex]
Therefore, the required polynomial expression is [tex]A=(2x-5)\times x[/tex] and its simplified form is [tex]A=2x^2-5x[/tex].