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