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Let's go over the division of polynomials by monomials step by step for each problem from your worksheet.

### 1. \( (66x^9 + 48x^4 - 72x^3) \div (6x^3) \)

- **Divide each term by \(6x^3\):**
  - \( \frac{66x^9}{6x^3} = 11x^6 \)
  - \( \frac{48x^4}{6x^3} = 8x \)
  - \( \frac{-72x^3}{6x^3} = -12 \)

- **Final result:**
  \[
  11x^6 + 8x - 12
  \]

---

### 2. \( (16x^6 - 18x^5 + 12x^3) \div (2x^3) \)

- **Divide each term by \(2x^3\):**
  - \( \frac{16x^6}{2x^3} = 8x^3 \)
  - \( \frac{-18x^5}{2x^3} = -9x^2 \)
  - \( \frac{12x^3}{2x^3} = 6 \)

- **Final result:**
  \[
  8x^3 - 9x^2 + 6
  \]

---

### 3. \( (64x^7 + 44x^4 - 32x^2) \div (4x^2) \)

- **Divide each term by \(4x^2\):**
  - \( \frac{64x^7}{4x^2} = 16x^5 \)
  - \( \frac{44x^4}{4x^2} = 11x^2 \)
  - \( \frac{-32x^2}{4x^2} = -8 \)

- **Final result:**
  \[
  16x^5 + 11x^2 - 8
  \]

---

### 4. \( \frac{36x^7 + 18x^4 + 12x^2}{6x^2} \)

- **Divide each term by \(6x^2\):**
  - \( \frac{36x^7}{6x^2} = 6x^5 \)
  - \( \frac{18x^4}{6x^2} = 3x^2 \)
  - \( \frac{12x^2}{6x^2} = 2 \)

- **Final result:**
  \[
  6x^5 + 3x^2 + 2
  \]

---

### 5. \( \frac{16x^7 + 28x^5 + 24x^4}{4x^4} \)

- **Divide each term by \(4x^4\):**
  - \( \frac{16x^7}{4x^4} = 4x^3 \)
  - \( \frac{28x^5}{4x^4} = 7x \)
  - \( \frac{24x^4}{4x^4} = 6 \)

- **Final result:**
  \[
  4x^3 + 7x + 6
  \]

---

### 6. \( \frac{x^7 + 8x^6 + 2x^5}{x^5} \)

- **Divide each term by \(x^5\):**
  - \( \frac{x^7}{x^5} = x^2 \)
  - \( \frac{8x^6}{x^5} = 8x \)
  - \( \frac{2x^5}{x^5} = 2 \)

- **Final result:**
  \[
  x^2 + 8x + 2
  \]

---

### Do you have any questions or would you like a deeper explanation of any of these problems?

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Here are 5 related questions that expand on this topic:

1. How would you divide polynomials by a binomial instead of a monomial?
2. What is the general rule for dividing polynomials with different degrees of terms?
3. How do you handle division when there is a remainder after dividing polynomials?
4. What happens if you divide a polynomial by a monomial that contains variables not present in the original polynomial?
5. Can synthetic division be used for dividing polynomials by monomials?

**Tip:** Always ensure that the degrees of the terms in both the numerator and the denominator are correctly matched when dividing polynomials to avoid calculation errors.

Dividing Polynomials by Monomials worksheet with problems like (66x^9 + 48x^4 - 72x^3) ÷ (6x^3)

Learn how to divide polynomials by monomials with detailed examples such as (66x^9 + 48x^4 - 72x^3) ÷ (6x^3). This worksheet is ideal for high school students in Grades 9-12, covering key algebraic concepts and exponent rules.

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