The volume of a rectangular prism is b^3 + 8b^2 + 19b + 12 cubic units, and its height is b + 3 units.

The area of the base of the rectangular prism is? square units.

The answer is (b² + 5b + 4).

The volume of a rectangular prism (V) is:

V = l · w · h (l - length, w - width, h - height)

The base of the rectangular prism is the product of length and width, so the area of the base is:

A = l · w

Since V = l · w · h and A = l · w, then:

V = A · h

It is given:

V = b³ + 8b² + 19b + 12

h = b + 3

⇒ b³ + 8b² + 19b + 12 = A · (b + 3)

⇒ A = (b³ + 8b² + 19b + 12) : (b + 3)

Now, we have to present the volume as multiplication of factors. One of the factors is b+3. So:

b³ + 8b² + 19b + 12 = (b · b² + 3b²) + (5b² + 15b) + (4b + 3·4) =

= b² (b + 3) + 5b (b + 3) + 4 (b + 3) =

= (b + 3) (b² + 5b + 4)

A = (b³ + 8b² + 19b + 12) : (b + 3) = (b + 3) (b² + 5b + 4) : (b + 3)

(b + 3) can be cancelled out:

A = (b² + 5b + 4)