Add the polynomial expressions 5z−2z2−4z+5 and 6z2+3−7z .(1 point)

Question

Responses

11z2+z−2
11 z squared plus z minus 2

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

4z2−z+8

Answer 1

To add the polynomial expressions \(5z - 2z^2 - 4z + 5\) and \(6z^2 + 3 - 7z\), we first simplify each expression before combining them.

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

2. Combine with the second polynomial: \[ (-2z^2 + z + 5) + (6z^2 - 7z + 3) \]

3. Combine like terms:

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

4. Final result: \[ 4z^2 - 6z + 8 \]

Since this does not match any of the given options, please verify the options or provide additional context.