Which example correctly demonstrates polynomial addition

To demonstrate polynomial addition, let's take two polynomial examples and show how to add them.

Let:
\[ P(x) = 3x^3 + 2x^2 + 5 \]
\[ Q(x) = 4x^3 + x + 7 \]

To add these two polynomials, we combine like terms:

1. First, organize the polynomials by their degree:
- For \( x^3 \): \( 3x^3 + 4x^3 = 7x^3 \)
- For \( x^2 \): \( 2x^2 \) (there is no corresponding term in \( Q(x) \))
- For \( x^1 \): \( 0 + x = x \) (the coefficient of \( x \) in \( P(x) \) is 0)
- For the constant term: \( 5 + 7 = 12 \)

Putting this together, we have:
\[
P(x) + Q(x) = 7x^3 + 2x^2 + x + 12
\]

Thus, the sum of the two polynomials \( P(x) \) and \( Q(x) \) is:
\[
7x^3 + 2x^2 + x + 12
\]

This is a correct demonstration of polynomial addition.