To demonstrate that the set of polynomials is closed under multiplication, we can multiply the polynomials \( (x^2 - 1)(-2x + 5) \):
1. **Distribute:**
\[
(x^2 - 1)(-2x + 5) = x^2 \cdot (-2x) + x^2 \cdot 5 - 1 \cdot (-2x) - 1 \cdot 5
\]
2. **Calculate each term:**
- \( x^2 \cdot (-2x) = -2x^3 \)
- \( x^2 \cdot 5 = 5x^2 \)
- \( -1 \cdot (-2x) = 2x \)
- \( -1 \cdot 5 = -5 \)
3. **Combine results:**
\[
-2x^3 + 5x^2 + 2x - 5
\]
4. **Conclusion:**
The product \( -2x^3 + 5x^2 + 2x - 5 \) is a polynomial, showing that the set of polynomials is closed under multiplication.