Question

The area of a rectangle is (x^3-5x^2+3x-15) and the width of the rectangle is (x^2+3) if area = length multiplied by width what is the length of the rectangle

Answer 1

length = x-5

Explanation:

To find the length of the rectangle, we can divide the given area by the width. Let's perform the division:

Given:

Area of the rectangle = (x³ - 5x² + 3x - 15)

Width of the rectangle = (x² + 3)

=> area = length × width => length = area / width

Substituting in our given values:

=> length = (x³ - 5x² + 3x - 15) / (x² + 3)

Now simplifying the equation. Start by factoring the numerator:

=> length = (x³ - 5x²) + (3x - 15) / (x² + 3)

=> length = x²(x - 5) + 3(x - 5) / (x² + 3)

=> length = (x - 5)(x²+ 3) / (x² + 3)

Canceling the common factor:

∴ length = x-5