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

Answer:

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

Step-by-step 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 = $\frac{(b^{3}+8b^{2}+19b+12) }{(b+3)}$

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)

Answer 2

Via synthetic division, we have

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

which is to say,

$\dfrac{b^3+8b^2+19b+12}{b+3}=b^2+5b+4$

is the area of the base.