Questions: If the area of the rectangle is 35x^2 - 50x + 8 square inches, and its length is 7x + 1 inches, find its width.

Solution Steps

To find the width of the rectangle, we can use the formula for the area of a rectangle, which is the product of its length and width. Given the area and the length, we can express the width as the area divided by the length. Therefore, we need to perform polynomial division of the area by the length to find the width.

The area \( A \) of the rectangle is given by the polynomial: \[ A = 35x^2 - 50x + 8 \] The length \( L \) of the rectangle is given by: \[ L = 7x + 1 \]

To find the width \( W \) of the rectangle, we use the formula: \[ W = \frac{A}{L} \] This requires performing polynomial division of \( A \) by \( L \).

Upon performing the polynomial division, we find: \[ W = 5x - 3 \] with a remainder of \( 11 \).

Final Answer