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

Question

5
𝑧
−
2
𝑧
2
−
4
𝑧
+
5
and 6z2+3−7z
6
𝑧
2
+
3
−
7
𝑧
.(1 point)
Responses

9z2−11z+8
9
𝑧
2
−
11
𝑧
+
8
9 z squared minus 11 z plus 8

4z2−z+8
4
𝑧
2
−
𝑧
+
8
4 z squared minus z plus 8

4z2−6z+8
4
𝑧
2
−
6
𝑧
+
8
4 z squared minus 6 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. Start with the first polynomial: \[ 5z - 2z^2 - 4z + 5 \] Combine the \( z \) terms: \[ (5z - 4z) = z \] So, the first polynomial simplifies to: \[ -2z^2 + z + 5 \]

2. Now, consider the second polynomial: \[ 6z^2 + 3 - 7z \] This is already in standard form.

3. Now we add the simplified first polynomial and the second polynomial together: \[ (-2z^2 + z + 5) + (6z^2 - 7z + 3) \]

4. Combine like terms:

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

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

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