https://file.aiquickdraw.com/mathbot/file/1730310603902dxk0yynj.jpg

To solve this problem, we need to subtract the second polynomial from the first:

\[
(2x^2 - 3x + 10) - (3x^2 - 5x + 12)
\]

Let's break down the steps:

1. **Distribute the negative sign** to each term in the second polynomial:
   \[
   = 2x^2 - 3x + 10 - 3x^2 + 5x - 12
   \]

2. **Combine like terms**:
   - For \(x^2\) terms: \(2x^2 - 3x^2 = -x^2\)
   - For \(x\) terms: \(-3x + 5x = 2x\)
   - For constant terms: \(10 - 12 = -2\)

So, the result is:
\[
-x^2 + 2x - 2
\]

The correct answer is:
\[
\boxed{-x^2 + 2x - 2}
\]

Would you like further details on any steps, or do you have additional questions?

### Related Questions
1. How do you add polynomials instead of subtracting?
2. What happens when subtracting polynomials with multiple variables?
3. Can you explain polynomial subtraction with fractions?
4. What is the degree of the resulting polynomial?
5. How do we verify the solution in polynomial subtraction?

### Tip
When subtracting polynomials, always distribute the negative sign across all terms of the second polynomial to avoid errors.

Subtract the polynomials: (2x^2 - 3x + 10) - (3x^2 - 5x + 12)

Explore the solution for subtracting polynomials (2x^2 - 3x + 10) - (3x^2 - 5x + 12). Learn how to distribute negative signs and combine like terms, designed for Grade 8 math students.

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