Answer:
The area of the rectangle can be expressed as:
10b^3 - 15b^2 + 14b
We know that the width of the rectangle is b - 1, so we can express the length of the rectangle in terms of b as:
length = area/width
length = (10b^3 - 15b^2 + 14b)/(b - 1)
To simplify this expression, we can use polynomial long division:
10b^2 - 5b - 9
___________________
b - 1 | 10b^3 - 15b^2 + 14b
- (10b^3 - 10b^2)
-------------------
-5b^2 + 14b
- (-5b^2 + 5b)
--------------
9b
- 9
-----
0
Therefore, the length of the rectangle is 10b^2 - 5b - 9. There is no remainder, so r = 0.
Answer: The length of the rectangle is 10b^2 - 5b - 9.