Answer :
Given:
Area of a rectangle = [tex]x^3-5x^2+3x-15[/tex]
Width of rectangle = [tex]x^2+3[/tex]
To find:
The length of the rectangle.
Solution:
The area of a rectangle is:
[tex]A=l\times w[/tex]
Where, l is length and w is the width.
It is can be written as:
[tex]\dfrac{A}{w}=l[/tex]
[tex]l=\dfrac{A}{w}[/tex]
Putting [tex]A=x^3-5x^2+3x-15[/tex] and [tex]w=x^2+3[/tex], we get
[tex]l=\dfrac{x^3-5x^2+3x-15}{x^2+3}[/tex]
[tex]l=\dfrac{x^2(x-5)+3(x-5)}{x^2+3}[/tex]
[tex]l=\dfrac{(x^2+3)(x-5)}{x^2+3}[/tex]
[tex]l=x-5[/tex]
Therefore, the length of the rectangle is [tex]x-5[/tex].