Question

Which example correctly demonstrates polynomial addition?(1 point) .

Answer 1

To demonstrate polynomial addition, you need to combine like terms from two or more polynomials. Here’s an example:

Suppose we have the following two polynomials:

1. \( P(x) = 3x^2 + 2x + 5 \)
2. \( Q(x) = 4x^2 + 3x + 1 \)

The addition of these two polynomials \( P(x) + Q(x) \) would be calculated as follows:

\[
P(x) + Q(x) = (3x^2 + 2x + 5) + (4x^2 + 3x + 1)
\]

Now, combine like terms:

- Combine \( x^2 \) terms: \( 3x^2 + 4x^2 = 7x^2 \)
- Combine \( x \) terms: \( 2x + 3x = 5x \)
- Combine constant terms: \( 5 + 1 = 6 \)

So the result of the polynomial addition is:

\[
P(x) + Q(x) = 7x^2 + 5x + 6
\]

This is a complete demonstration of polynomial addition.