The volume of a rectangular prism is b3 + 8b2 + 19b + 12 cubic units, and its height is b + 3 units. the area of the base of the rectangular prism is square units.

Given:

The volume of the rectangular prism is 

,

the height is h=(b+3)

1. The volume of a rectangular prism is (base area)*height

also, notice that the volume is a third degree polynomial, the height is a 1st degree polynomial, so the base area must be a 2nd degree polynomial, whose coefficients we don't know yet.
Let this quadratic polynomial be 

 
2



notice that   is the product of the largest 2 terms:  and b, so m must be 1

also, notice that 12 is the product of the constants, k and 3

so k*3=12, this means k=4

3
we write the above equality again:





=

4
now compare the coefficient with the left side:



8=n+3

n=5

substituting n=5: 

the base area is