The area of a rectangle is 5x^3+19x^2+6x-18 with length x + 3. using synthetic division, what is the width of the rectangle?

To compute for the area of the rectangle, we multiply the dimensions so if  we need to find the width of the rectangle, we have



Thus, given an area of (5x³ + 19x² + 6x - 18) and a length of (x + 3), to find the width, we have

width = (5x³ + 19x² + 6x - 18) / (x + 3)

Through the coefficients of the polynomial, we can apply synthetic division to find the quotient as shown below.

5  19  6  -18 | -3
   -15 -12  18
_____________
5   4   -6  0

Thus, the given values below the line are the coefficients of the width. So, we have the rectangle's width as (5x² + 4x - 6) units.

 (5x² + 4x - 6) units