Add the polynomial expressions 5z−2z2−4z+5 and 6z2+3−7z .(1 point) Responses 9z2−11z+8 9 z squared minus 11 z plus 8 4z2−6z+8 4 z squared minus 6 z plus 8 11z2+z−2 11 z squared plus z minus 2 4z2−z+8

Answer 1

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

1. The first polynomial can be rewritten as: \[ -2z^2 + (5z - 4z) + 5 = -2z^2 + z + 5 \]

2. The second polynomial can be written as: \[ 6z^2 + (-7z) + 3 = 6z^2 - 7z + 3 \]

Now, let's combine both polynomials: \[ (-2z^2 + z + 5) + (6z^2 - 7z + 3) \]

Next, we combine the like terms:

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

Putting it all together, the sum is: \[ 4z^2 - 6z + 8 \]

So the final answer is: \[ \boxed{4z^2 - 6z + 8} \]