To add the polynomials $(3 - 2x + 3x^2)$ and $(7 + 6x - 2x^2)$, follow these steps:

Step 1: Arrange the terms of each polynomial in standard form (order terms by decreasing powers of $x$):

• $(3 - 2x + 3x^2)$ becomes $3x^2 - 2x + 3$
• $(7 + 6x - 2x^2)$ becomes $-2x^2 + 6x + 7$

Step 2: Add the corresponding terms:

• For $x^2$-terms: $3x^2 + (-2x^2) = x^2$
• For $x$-terms: $-2x + 6x = 4x$
• For constant terms: $3 + 7 = 10$

Step 3: Combine the results:

The sum of the polynomials is:

$x^2 + 4x + 10$

Final Answer:

$(3 - 2x + 3x^2) + (7 + 6x - 2x^2) = x^2 + 4x + 10$

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Would you like further clarification or examples? Here are some related questions to explore:

1. How do you subtract polynomials?
2. What happens when you add polynomials with different powers of $x$?
3. Can you simplify expressions with higher-degree polynomials?
4. What is the difference between adding and multiplying polynomials?
5. How do you factor polynomials after performing operations on them?

Tip: When adding or subtracting polynomials, always line up terms with the same degree to simplify the process.