Which example correctly demonstrates polynomial addition?(1 point)

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

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

Suppose we have the following two polynomials:
- Polynomial A: \( 3x^2 + 2x + 5 \)
- Polynomial B: \( 4x^2 + 3x + 1 \)

To add these polynomials, you would proceed as follows:

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

Combine like terms:

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

Putting it all together, the result of the polynomial addition is:

\[
7x^2 + 5x + 6
\]

So, the example \( (3x^2 + 2x + 5) + (4x^2 + 3x + 1) = 7x^2 + 5x + 6 \) correctly demonstrates polynomial addition.