Question

The area of a rectangle is with length x 3. using synthetic division, what is the width of the rectangle?

1. The width of the rectangle using synthetic division is; 5x² + 4x – 6.
What is the width of the rectangle whose area is 5x³+19x²+6x-18?
From the task content; the width of the rectangle whose area and length are as given can be evaluated as follows;
Area = Length × width
Hence, width = Area/length.
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.
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The complete question is –
The area of a rectangle is 5×3+19×2+6x-18 with length x + 3. Using synthetic division, what is the width of the rectangle?