Question

And the polynomial expression 5z - 2z squared minus 4z + 5 and 6z squared plus 3 - 7z

Answer 1

Let's simplify and combine the given polynomial expressions:

1. **First expression**: \( 5z - 2z^2 - 4z + 5 \)

Combine like terms:
- Combine \( 5z \) and \( -4z \) which gives \( 1z \) or just \( z \).
- So the expression simplifies to:
\[
-2z^2 + z + 5
\]

2. **Second expression**: \( 6z^2 + 3 - 7z \)

This expression is already simplified, but we can reorder it in standard polynomial form (highest degree first):
\[
6z^2 - 7z + 3
\]

Now, this results in two separate polynomial expressions:
- First expression: \( -2z^2 + z + 5 \)
- Second expression: \( 6z^2 - 7z + 3 \)

If you want to combine these two expressions (i.e., add them together), we can do that as follows:

**Combining both expressions**:
\[
(-2z^2 + z + 5) + (6z^2 - 7z + 3)
\]

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

So the result of combining both polynomials is:
\[
4z^2 - 6z + 8
\]

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