The image includes two exercises related to polynomials. Here's a breakdown of each exercise:

Exercise 24

Given the polynomials $P(x) = 3x^4 - 2x^2 + x + 1$ and $Q(x) = -5x^3 + 7x^2 - 3x + 8$, perform the following:

a) Find the degrees of $P(x)$ and $Q(x)$:
The degree of a polynomial is the highest power of $x$ with a non-zero coefficient.

b) Determine the degree of $P(x) + Q(x)$:
Add $P(x)$ and $Q(x)$, then find the highest degree term in the resulting polynomial. Does this degree match either the degree of $P(x)$ or $Q(x)$?

c) Write two polynomials $R(x)$ and $S(x)$, such that their sum has a degree that does not coincide with the degree of either polynomial.
Create $R(x)$ and $S(x)$ with specific terms that fulfill this condition.

Exercise 25

Perform the operations with the polynomials $P(x) = 5x^2 - 2x + 1$, $Q(x) = 2x^3 - 7$, $R(x) = 7x^2 - 3x + 2$, and $S(x) = -5x^2 + 2x - 1$:

Examples:
a) $P(x) + Q(x) + R(x)$
b) $P(x) + Q(x) + S(x)$
c) $P(x) + Q(x) - R(x)$
... and so on, completing all the provided combinations.

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Questions for Exploration

1. How do the rules for polynomial addition and subtraction affect the resulting degree of the polynomial?
2. Can a sum of two polynomials have a degree lower than the highest degree among them?
3. How does the leading coefficient impact the behavior of polynomials?
4. Why is the degree of a polynomial an important characteristic?
5. How can you check polynomial operations for correctness?

Tip: When adding or subtracting polynomials, always align terms by their degree to avoid mistakes.