If the area of the rectangle is 35x^2-53x-18 and its length is 7x+2 inches, find its width

5x - 9

Step-by-step explanation:

The area of the rectangle is:

(1)

The area of the rectangle is the product of length (L) and width (W):

where , and the width must be in the form .

We need to find the values of a and b. If we calculate the product of L and W, we get:

We know that this equation must be equivalent to (1), so we immediately see that:

- the coefficient of the second order term, , must be 35, so

- the zero-order term must be equal to -18, so we have

- We can verify that using a=5 and b=-9, the coefficient of the first-order term corresponds to -53:

So, the width is

W = 5x - 9