Final answer:
To find the missing side length of the rectangle, divide the area equation by the known side length. Use synthetic division or long division to simplify the equation and find the missing side length.
Step-by-step explanation:
To find the missing side length of the rectangle, we need to find the other factor in the area equation. The area of a rectangle is given by the formula A = length × width. In this case, we are given the area as x^3 + 3x^2 + 5x + 3 and one of the side lengths as x + 1. We can set up the equation: (x + 1) × ? = x^3 + 3x^2 + 5x + 3. To solve for the missing side length, we divide both sides of the equation by x + 1. This gives us the equation: ? = (x^3 + 3x^2 + 5x + 3) / (x + 1). To simplify the equation, we can use synthetic division or long division to divide x^3 + 3x^2 + 5x + 3 by x + 1. The quotient will give us the missing side length.