The polynomial 4x3 -8x2 -11x - 3 represents the volume in cubic feet of a rectangular fish tank,. The area of the base can be expressed by the polynomial 4x2 + 4x + 1. Find an expression for the height of the fish tank.

Select one:
a. 2x + 1
b. x - 3
c. x + 3
d. x2 + 2x + 1

Question

The polynomial 4x3 -8x2 -11x - 3 represents the volume in cubic feet of a rectangular fish tank,.  The area of the base can be expressed by the polynomial 4x2 + 4x + 1.  Find an expression for the height of the fish tank.

Select one:
a. 2x + 1
b. x - 3
c. x + 3
d. x2 + 2x + 1

1645323 · Answer

@terenzreignz

1645323 · Answer

@mathmale

mathmale · Answer

Hello, 1645323!
Recall that the volume of a rectangular 3D figure  is (length) * (width) * ( height).

Supposing the volume is V = L*W*H, how would you solve this equation for H?

mathmale · Answer

Hint:  divide both sides of this equation by what quantity?

1645323 · Answer

the area of the base?

mathmale · Answer

Right.  

In this problem you are given a polynomial expression which represents the volume of a rectangular prism, along with one that represents the area of the base.  Using my previous question as a guide, how would you determine the height of this rectangular prism?

mathmale · Answer

V = 4x3 -8x2 -11x - 3
Area of base = 4x2 + 4x + 1

A formula for the height is ... ?

1645323 · Answer

idk what is it?@mathmale

mathmale · Answer

Take V and divide it by the Area of the Base:
          4x3 -8x2 -11x - 3
H = ------------------
            4x2 + 4x + 1

You could use long division here.  An alternative approach would be synthetic division.  Use whichever is the more familiar to you.

1645323 · Answer

its x-3

mathmale · Answer

____________________
4x^2+4x+1 |   4x3 -8x2 -11x - 3

Yes, that's x-3.  Congrats!  Nice work!