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

Question

and 6z2+3−7z
.(1 point)
Responses

11z2+z−2
11 z squared plus z minus 2

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

Answer 1

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

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

2. Now, combine with the second polynomial: \[ z - 2z^2 + 5 + 6z^2 + 3 - 7z \]

3. Group similar terms:

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

4. Combine all the terms: \[ 4z^2 - 6z + 8 \]

Therefore, the sum of the two polynomial expressions is:

\[ \boxed{4z^2 - 6z + 8} \]

So, the correct response is: 4z2−6z+8.