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

Question

and 6z^2+3−7z
.(1 point)

Answer 1

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

1. First expression: \[ 5z - 2z^2 - 4z + 5 \] Combine like terms: \[ (-2z^2) + (5z - 4z) + 5 = -2z^2 + z + 5 \]

2. Second expression: \[ 6z^2 + 3 - 7z \] This expression is already simplified.

Now, we add the two simplified expressions: \[ (-2z^2 + z + 5) + (6z^2 - 7z + 3) \]

Now, combine the like terms:

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

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

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