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The question asks for the product of the solutions of the polynomial equation:

\[
x^3 - 4x^2 - 7x + 10 = 0
\]

By Vieta's formulas, for a cubic equation of the form \( ax^3 + bx^2 + cx + d = 0 \), the product of the solutions is given by:

\[
\text{Product of roots} = \frac{-d}{a}
\]

Here, the equation is:

\[
x^3 - 4x^2 - 7x + 10 = 0
\]

So:
- \( a = 1 \)
- \( b = -4 \)
- \( c = -7 \)
- \( d = 10 \)

Using Vieta's formula:

\[
\text{Product of roots} = \frac{-d}{a} = \frac{-10}{1} = -10
\]

Thus, the product of the solutions is \(-10\).

### Answer: A. \(-10\)

Would you like more details or have any other questions?

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Here are five related questions to deepen your understanding:
1. How does Vieta's formula work for quadratic equations?
2. What is the sum of the roots of a cubic equation?
3. How can you factor a cubic equation to find its solutions directly?
4. What does the discriminant tell you about the nature of the roots in cubic equations?
5. How would the solution change if the leading coefficient were not 1?

**Tip:** Vieta's formulas are extremely useful for quickly finding relationships between the roots of polynomials without actually solving the equation!

What is the product of the solutions of x^3 - 4x^2 - 7x + 10 = 0?

Find the product of the solutions for the cubic equation x^3 - 4x^2 - 7x + 10 = 0 using Vieta's formulas. This problem explores key algebraic concepts such as polynomials, cubic equations, and root relationships. Suitable for students in Grades 10-12.

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