add the polynomial expression 5z - 2z^2 - 4z + 5 and 6z^2 + 3 - 7z

Answer 1

To add the polynomial expressions \( 5z - 2z^2 - 4z + 5 \) and \( 6z^2 + 3 - 7z \), we first combine like terms from both expressions.

1. Combine like terms from the first expression: \[ 5z - 4z - 2z^2 + 5 = (5z - 4z) + (-2z^2) + 5 = 1z - 2z^2 + 5 = -2z^2 + z + 5 \]

2. Now write the second expression: \[ 6z^2 - 7z + 3 \]

3. Now add both expressions: \[ (-2z^2 + z + 5) + (6z^2 - 7z + 3) \]

4. Combine like terms:

   • For \( z^2 \) terms: \[ -2z^2 + 6z^2 = 4z^2 \]
   • For \( z \) terms: \[ z - 7z = -6z \]
   • For the constant terms: \[ 5 + 3 = 8 \]

5. Putting it all together, we have: \[ 4z^2 - 6z + 8 \]

Therefore, the sum of the polynomial expressions is: \[ \boxed{4z^2 - 6z + 8} \]