Which example correctly demonstrates polynomial addition?(1 point)

1 answer

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.