Add the polynomial expressions 5z - 2z^2 - 4z + 5 and 6z^2 + 3 - 7z.

Question

9z^2 - 11z + 8
4z^2 - 6z + 8
4z^2 - z + 8
11z^2 + z - 2

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

2. Write the second polynomial: \[ 6z^2 + 3 - 7z = 6z^2 + (-7z) + 3 \]

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

Now, add the like terms:

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

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

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