Emily collects and trades rocks. She starts with 8x2 rocks, for some number x, and then buys 7x4. She then trades away x5, then gives away 9x, and finally sells another 5 rocks. Write an expression for the number of rocks Emily now has in standard form.
A.	−9x + 8x2 + 7x4 − 5 − x5
B.	8x2 − 5 + 7x4 − 9x − x5
C.	−x5 + 7x4 + 8x2 − 9x − 5
D.	−5 − 9x + 8x2 + 7x4 − x5

To solve this problem, we need to write an expression for the number of rocks Emily has after performing all the operations. Let's break down each step:

1. **Initial rocks:** Emily starts with \(8x^2\) rocks.
2. **Rocks bought:** She buys \(7x^4\) rocks.
3. **Rocks traded away:** She trades away \(x^5\) rocks.
4. **Rocks given away:** She gives away \(9x\) rocks.
5. **Rocks sold:** She sells 5 rocks.

The expression that represents the total number of rocks Emily has is the sum of the rocks she starts with and buys, minus the rocks she trades away, gives away, and sells:

\[
8x^2 + 7x^4 - x^5 - 9x - 5
\]

Now, let's write this expression in standard form, where the terms are ordered from the highest power of \(x\) to the lowest:

\[
- x^5 + 7x^4 + 8x^2 - 9x - 5
\]

This matches option **C**.

So, the correct answer is **C**.

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Would you like any further details or have any other questions? Here are 5 questions that might interest you:

1. How do we determine the standard form of a polynomial?
2. Can you explain the process of combining like terms in polynomials?
3. How do the degrees of terms in a polynomial affect its graph?
4. What happens if Emily starts with a negative number of rocks?
5. How do you solve a polynomial equation if it's set equal to zero?

**Tip:** When writing polynomials in standard form, always arrange the terms in decreasing order of their exponents.

Explore Emily's rock collection algebraic expression problem: starting with 8x^2 rocks, buying 7x^4, trading x^5, giving away 9x, and selling 5 rocks. Solve the expression -x^5 + 7x^4 + 8x^2 - 9x - 5.

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