Question

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. (Hint: volume = length × width × height) NextReset

Answer 1

Via synthetic division, we have

-3 | 1 8 19 12
... | -3 -15 -12
= = = = = = = = = = = =
... | 1 5 4 0

which is to say,


`(b^3+8b^2+19b+12)/(b+3)=b^2+5b+4`

is the area of the base.

Answer 2

Therefore, the area of the base will be (b² + 5b +4)

Explanation:

The volume of rectangular prism has been given as (b³+8b²+19b+12) and height is (b+3) units.

We have to calculate the area of the base of the given prism

As we know the formula of volume of prism

⇒ V = (Area of the base) × Height

or Area of the base = V/ height

⇒ Area =
`((b^(3)+8b^(2)+19b+12) )/((b+3))`

To solve this we will use synthetic division

-3 1 8 19 12

1 -3 -15 -12

1 5 4 0

Therefore, quotient of the division will be the area of the base,

which is (b²+5b+4)

Therefore, the area of the base will be (b² + 5b +4)