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: $14x^2 - 6x + 16$.

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!