SOLUTION: Let us use the following problem statement, to discuss differences between a term and a factor? Let us consider the price of a cube shaped stone of length R inches. The cost

Question 80446: Let us use the following problem statement, to discuss differences between a term and a factor?
Let us consider the price of a cube shaped stone of length R inches. The cost of an unpolished stone is proportional to its weight which is proportional to cube of its length, i.e. R*R*R or R^3 cubic inches.

Assuming that it cost $1000 for one cubic inch of raw stone, we can write the cost of one raw stone as 1000R^3. e.g. if R is 2 inches, the cost of raw stone is 1000 * 2^3 or $8000.

Let cost of polishing a square inch of the surface area of the rock is $100. Noting that the surface area of rock is proportional to the square of length, i.e. R^2 we have the cost of polishing the stone as 600R^2 (note there are 6 faces to a cube). In the above example where R is 2 inches, the cost of polishing is 600 * 2^2 or $2400.

Assuming there is no other cost, the cost of a finished stone would require summing up the cost of raw stone (by weight) and cost of polishing.
Write down an expression for the cost of the finished stone of length R and identify the different terms in it.
Can you factor these terms? Is there any factor common to different terms here?
What is the expression for cost of 5 finished stones of length X?

Answer by CubeyThePenguin(3113) (Show Source): You can put this solution on YOUR website!
cost of 1 raw stone = 1000x^3
cost to polish stone = 600x^2

5 stones: 5000x^3 + 3000x^2
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