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The problem appears to involve performing polynomial division. Specifically, the expression shown is:

\[
x - 1 \quad \text{divided by} \quad x^3 + 2x^2 + 2x
\]

The task is to begin by writing the expression in a specific form, and it looks like you are required to fill in two blanks to complete the setup.

### Steps:
1. **Identify the Division Setup**: Polynomial division is often written as:

   \[
   \frac{x^3 + 2x^2 + 2x}{x - 1}
   \]

2. **Start the Division**: You would start the long division by dividing the leading term of the dividend, \(x^3\), by the leading term of the divisor, \(x\).

- \(x^3 \div x = x^2\), so the first term in the quotient is \(x^2\).

Let me know if you would like a detailed step-by-step process for the polynomial division!

### Follow-up questions:
1. What happens when dividing \(x^3\) by \(x\)?
2. What would be the next step after obtaining \(x^2\) as the first term?
3. How do you subtract the product from the original polynomial during division?
4. What is the purpose of aligning terms in polynomial long division?
5. Can polynomial division always result in a polynomial quotient?

### Tip:
When performing polynomial division, always ensure that the terms are written in descending order of their degree for easier alignment.

To perform the division x - 1 divided by x^3 + 2x^2 + 2x, begin by writing the expression in a specific form.

This example illustrates the steps to divide the polynomial x^3 + 2x^2 + 2x by x - 1. Learn how to perform long division on polynomials by following the division of x^3 by x. Suitable for high school students in Grades 10-12.

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