explain how

you can determine the height of a three-dimensional rectangular object given its

area and volume.

Hi, Henriettas.

If I may add to Ronald's example ...

If the volume did happen to be (8x^3 + 8x^2 - 8x - 5), and the area happened to be (4x^2 + 2x - 5), we could solve for the height by factoring. But if you're looking for directions for polynomial long division, your problem might look something like this:

.

4x^2 + 2x - 5 ) 8x^3 + 8x^2 - 8x - 5

To divide these polynomials, start by looking at how many times 4x^2 "goes into" 8x^3. You can quickly figure that out by writing 8x^3 over 4x^2 and reducing:

8x^3

4x^2

This is 2x. Now place the 2x in the quotient:

____ 2x .

4x^2 + 2x - 5 ) 8x^3 + 8x^2 - 8x - 5

Now multiply the 2x by all three terms of the divisor (4x^2 + 2x - 5) and write them under the dividend (8x^3 + 8x^2 - 8x -5), and be sure to subtract:

______ 2x .

4x^2 + 2x - 5 ) 8x^3 + 8x^2 - 8x - 5

- ( 8x^3 + 4x^2 -10x ) .

___ 2x .

4x^2 + 2x - 5 ) 8x^3 + 8x^2 - 8x - 5

- 8x^3 - 4x^2 +10x .

4x^2 + 2x - 5

Now, do this division process again...

_____ 2x + 1

4x^2 + 2x - 5 ) 8x^3 + 8x^2 - 8x - 5

- 8x^3 - 4x^2 +10x .

4x^2 + 2x - 5

- (4x^2 + 2x - 5)

________ 2x + 1

4x^2 + 2x - 5 ) 8x^3 + 8x^2 - 8x - 5

- 8x^3 - 4x^2 +10x .

4x^2 + 2x - 5

- 4x^2 - 2x + 5

0

Since there is no remainder, the answer to Ronald's problem is again 2x + 1

Hope this helps with polynomial long division, Henriettas.

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