Question

Which of the following is the simplified form of
-10x^2+20x+80/x+2
?

A
x+4x+4x+4

B
x−4x-4x−4

C
−10x+40-10x+40−10x+40

D
10x−4010x-4010x−40

Answer 1

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?