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To solve this problem, we need to perform polynomial division. The total number of sheets is given by the polynomial:

\[
P(x) = x^3 - 61x - 7x^2 + 200
\]

Mirtha wants to distribute these sheets among \(x - 11\) students, so we divide \(P(x)\) by \(x - 11\).

Let's perform the division. I'll calculate it now.The result of dividing \( P(x) = x^3 - 7x^2 - 61x + 200 \) by \( x - 11 \) gives the quotient:

\[
x^2 + 4x - 17
\]

and the remainder is:

\[
13
\]

This means each student will receive \( x^2 + 4x - 17 \) sheets, and Mirtha will be left with 13 sheets. Therefore, the correct answer is:

**Option A: \( x^2 + 4x - 17 \) and 13**.

Would you like a detailed explanation of the polynomial division process or have any other questions?

Here are five follow-up questions related to this problem:
1. How is polynomial division different from regular division?
2. Why is the remainder important in polynomial division?
3. What does the quotient represent in this context?
4. How can synthetic division be used for such problems?
5. Can you describe how polynomial long division works step by step?

**Tip:** When dividing polynomials, always check your work by multiplying the quotient by the divisor and adding the remainder to ensure you get the original polynomial.

Mirtha tiene x^3 - 61x - 7x^2 + 200 hojas bond A4 y desea repartir entre sus x - 11 estudiantes del colegio en forma equitativa, ¿cuántas hojas le correspondería a cada estudiante y cuántas hojas le sobraría a Mirtha?

Learn how to solve the polynomial division problem where Mirtha has x^3 - 7x^2 - 61x + 200 sheets of A4 paper and distributes them among x - 11 students. Understand the quotient and remainder involved in this step-by-step division process, suitable for Grades 9-12.

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