Math Problem Statement
Solution
The problem states that the volume of a rectangular prism is , and the area of the base is . To find the height of the prism, we use the fact that the volume is the product of the base area and the height, i.e.,
Thus, the height can be found by dividing the volume by the base area:
Now, let's perform this division:
Step 1: Polynomial long division
We need to divide by .
- Divide the leading term by , which gives .
- Multiply by , resulting in .
- Subtract this from the original polynomial:
Step 2: Repeat the division process
Now divide by , which gives .
- Multiply by , resulting in .
- Subtract:
So the result of the division is:
This matches the third answer choice:
Final Answer:
The correct answer is the third option.
Would you like further details on any step?
Here are some related questions:
- How do you perform polynomial long division in general?
- What is the significance of dividing polynomials in finding the height of prisms?
- Can you apply this method to other types of solids?
- How would the problem change if the base area were a different polynomial?
- Can the height of a prism always be found this way?
Tip: When dividing polynomials, always align like terms to avoid mistakes in subtraction.
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Math Problem Analysis
Mathematical Concepts
Polynomial Division
Volume of Rectangular Prisms
Algebra
Formulas
Volume = Base Area * Height
Height = Volume / Base Area
Theorems
Polynomial Long Division
Suitable Grade Level
Grades 10-12
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