https://file.aiquickdraw.com/mathbot/file/17296974832007ql3zx67.jpg

Let's first solve the addition problem shown in the image:

The expression is:

\[
(2x^3 + 5x - 16) + (4x^3 - 10x^2 - 2x)
\]

### Step 1: Combine like terms

- For \(x^3\) terms: \(2x^3 + 4x^3 = 6x^3\)
- For \(x^2\) terms: There is only \(-10x^2\), so it stays \(-10x^2\)
- For \(x\) terms: \(5x - 2x = 3x\)
- For constant terms: \(-16\) (no other constants to combine)

### Final result:

\[
6x^3 - 10x^2 + 3x - 16
\]

The correct answer is **\(6x^3 - 10x^2 + 3x - 16\)**, which matches the third option in the image.

Would you like more details on the process or clarification on a specific step?

Here are 5 follow-up questions to expand on this:

1. What are the general rules for adding polynomials?
2. Can you combine terms with different exponents, like \(x^3\) and \(x^2\)?
3. How do you handle subtraction when combining polynomials?
4. What is the next step if there were fractions involved in the polynomial terms?
5. Can this method be used for subtracting polynomials as well?

**Tip:** Always group like terms together (those with the same exponent) to simplify polynomial addition or subtraction.

Add (2x^3 + 5x - 16) + (4x^3 - 10x^2 - 2x)

Learn how to add polynomials like (2x^3 + 5x - 16) + (4x^3 - 10x^2 - 2x). This problem focuses on combining like terms for powers of x, perfect for students in Grades 7-10 who are studying algebra and polynomial operations.

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