Question

The volume of a rectangular prism is (x4 + 4x3 + 3x2 + 8x + 4), and the area of its base is (x3 + 3x2 + 8). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?

Answer 1

Thank you for asking this question. Here is your answer:

In order to find the height we will divide the polynomials.

We will divide the following equation:

x⁴+ 4x³ + 3x² + 8x + 4 by x³ + 3x² + 8

And then we will mutiply x³ + 3x² + 8 by x

And the second step would be we will subtract it from the other polynomial

And the result for that would be :

x³ + 3x² + 4

And now we will multiply x³ + 3x² + 8 by 1 and when we will do the subtraction, the result would be:  -4

So the height is  (x + 1)

The final answer for this question is (x + 1)

If there is any confusion please leave a comment below.