In the image, the fourth question from the list under "Add the following polynomials" reads:

$\frac{2}{3}x^2 - \frac{1}{3}, x^3 + 5, \frac{4}{3}x^2 + 2x^3 - 3, \frac{5}{3}x^2 - \frac{4}{3}x + 1$

We need to add these polynomials. Let's break this down into steps, making sure to combine like terms, which are terms that involve the same powers of $x$.

1. Identify and combine constant terms.
2. Identify and combine terms involving $x$.
3. Identify and combine terms involving $x^2$.
4. Identify and combine terms involving $x^3$.

Let's add these polynomials step by step. I'll calculate the sum now.The sum of the given polynomials is:

$3x^3 + \frac{11}{3}x^2 - \frac{4}{3}x + \frac{8}{3}$

Here’s a breakdown of how each term was combined:

• For $x^3$: $x^3 + 2x^3 = 3x^3$
• For $x^2$: $\frac{2}{3}x^2 + \frac{4}{3}x^2 + \frac{5}{3}x^2 = \frac{11}{3}x^2$
• For $x$: $- \frac{4}{3}x$
• Constants: $- \frac{1}{3} + 5 - 3 + 1 = \frac{8}{3}$

Would you like further details or have any questions on this? Here are some possible questions you might consider:

1. How to find the coefficients for each term?
2. What if the powers of $x$ were different?
3. How do negative signs affect the addition of terms?
4. How to check if you have combined all like terms correctly?
5. Can you show a graphical representation of these polynomials?

Tip: Always align the like terms vertically when adding polynomials manually to avoid missing any term or making errors in sign.