https://file.aiquickdraw.com/mathbot/file/1728696976735v78ep20k.jpg

Let's work through the problem from the image step by step.

We are asked to add the following polynomials:

\[
(7x^2 - 3x + 8) + (-2x^2 - 5 - 3x + 13 + 9x^2)
\]

### Step 1: Combine like terms.

1. **For \(x^2\) terms**:
   \[
   7x^2 + (-2x^2) + 9x^2 = 7x^2 - 2x^2 + 9x^2 = 14x^2
   \]

2. **For \(x\) terms**:
   \[
   -3x + (-3x) = -3x - 3x = -6x
   \]

3. **For constant terms**:
   \[
   8 + (-5) + 13 = 8 - 5 + 13 = 16
   \]

### Step 2: Write the result.

Combining everything, we get:

\[
14x^2 - 6x + 16
\]

### Answer:

The correct option is **D: \(14x^2 - 6x + 16\)**.

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Would you like any further details or clarifications?

Here are 5 related questions you might explore:
1. How do you subtract polynomials?
2. What are the different methods of combining like terms?
3. How do you solve for roots of a quadratic equation like \(14x^2 - 6x + 16\)?
4. What is the process for multiplying polynomials?
5. How do you graph polynomial functions?

**Tip**: Always arrange terms in descending order of exponents when simplifying polynomials for easier readability!

Add the following polynomials: (7x^2 - 3x + 8) + (-2x^2 - 5 - 3x + 13 + 9x^2)

Learn how to add polynomials by combining like terms with the example (7x^2 - 3x + 8) + (-2x^2 - 5 - 3x + 13 + 9x^2). This algebraic problem involves adding x^2 terms, x terms, and constants, suitable for students in Grades 8-10.

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