The fourth subpart of the first question (from the image provided) asks you to Add the following polynomials:

$\frac{4}{3} x^2 + 5 + \frac{5}{3} x^2 + 4$

To solve this, we follow these steps:

Step 1: Combine like terms

• The terms containing $x^2$ are $\frac{4}{3} x^2$ and $\frac{5}{3} x^2$.
• The constant terms are $5$ and $4$.

Step 2: Add the $x^2$ terms

$\frac{4}{3} x^2 + \frac{5}{3} x^2 = \frac{4 + 5}{3} x^2 = \frac{9}{3} x^2 = 3x^2$

Step 3: Add the constant terms

$5 + 4 = 9$

Step 4: Write the final expression

Now combine the result from Step 2 and Step 3: $3x^2 + 9$

Thus, the sum of the given polynomials is: $\boxed{3x^2 + 9}$

Would you like more details on this solution, or help with any other parts of the question?

Here are 5 related questions:

1. How do you subtract polynomials with similar terms?
2. What is the general rule for adding fractions with variables?
3. How do you combine terms with different powers of the same variable?
4. Can we multiply polynomials directly after adding them?
5. How does the degree of a polynomial affect its simplification?

Tip: When adding polynomials, always group like terms (terms with the same variables and exponents) to simplify the process.