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
[tex] width = \frac{Area}{length} [/tex]
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.
Answer: (5x² + 4x - 6) units
