Add the polynomial expressions 5z−2z2−4z+5

Question

and 6z2+3−7z
.(1 point)
Responses

4z2−6z+8
4 z squared minus 6 z plus 8

4z2−z+8
4 z squared minus z plus 8

9z2−11z+8
9 z squared minus 11 z plus 8

11z2+z−2

Answer 1

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

1. Rewrite the first expression: \[ 5z - 2z^2 - 4z + 5 = -2z^2 + (5z - 4z) + 5 = -2z^2 + z + 5 \]

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

3. Now add the two simplified expressions together: \[ (-2z^2 + z + 5) + (6z^2 - 7z + 3) \] Combine the like terms:

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

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

Thus, the answer is:

4z² - 6z + 8.