Which of the following is the simplified form of

To simplify the expression \(-10x^2 + 20x + 80\) divided by \(x + 2\), we will perform polynomial long division.

1. Divide the first term of the numerator by the first term of the denominator: \[ \frac{-10x^2}{x} = -10x \]

2. Multiply the entire divisor \(x + 2\) by \(-10x\): \[ -10x(x + 2) = -10x^2 - 20x \]

3. Subtract this result from the original polynomial: \[ (-10x^2 + 20x + 80) - (-10x^2 - 20x) = 20x + 20x + 80 = 40x + 80 \]

4. Now, we divide the new leading term \(40x\) by the leading term of the divisor \(x\): \[ \frac{40x}{x} = 40 \]

5. Multiply the entire divisor \(x + 2\) by \(40\): \[ 40(x + 2) = 40x + 80 \]

6. Subtract this from \(40x + 80\): \[ (40x + 80) - (40x + 80) = 0 \]

Now, we have completed the division which yields: \[ -10x + 40 \]

Thus, the expression \(\frac{-10x^2 + 20x + 80}{x + 2}\) simplifies to \(-10x + 40\).

Reviewing the answer choices:

A: \(x + 4x + 4\)
B: \(x - 4x - 4\)
C: \(-10x + 40 - 10x + 40\)
D: \(10x - 40\)

The correct simplified form of the expression is not listed among the options provided, but the answer is: \(-10x + 40\).

Can you check if there was a typo or some miscommunication in the provided answer choices?