The area of a shape is the amount of space it occupies.
The length of the rectangle is x - 5
The given parameters are:
[tex]Area = x^3 - 5x^2 + 3x - 15[/tex]
[tex]Width = x^2 + 3[/tex]
The area of a rectangle is:
[tex]Area = Length \times Width[/tex]
Make Length the subject
[tex]Length = \frac{Area}{Width}[/tex]
Substitute known values
[tex]Length = \frac{x^3 - 5x^2 + 3x - 15}{x^2 + 3}[/tex]
Factorize the numerator
[tex]Length = \frac{x^2(x - 5) + 3(x - 5)}{x^2 + 3}[/tex]
Factor out x - 5
[tex]Length = \frac{(x^2 + 3) (x - 5)}{x^2 + 3}[/tex]
Cancel out common factors
[tex]Length = x - 5[/tex]
Hence, the length of the rectangle is x - 5
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