Question

Which of the following is the simplified form of -10 { x }^{ 2 } +20x+80 /x+2
A. 10x-40
b x+4
c. -10x+40
x-4

Answer 1

To simplify the expression \(-10x^2 + 20x + 80\) divided by \(x + 2\), we can follow these steps:

1. **Factor the numerator**: First, we'll take the numerator \(-10x^2 + 20x + 80\) and factor it.

Factor out \(-10\):
\[
-10(x^2 - 2x - 8)
\]

Now, we need to factor \(x^2 - 2x - 8\). We look for two numbers that multiply to \(-8\) and add to \(-2\). The numbers that satisfy this are \(2\) and \(-4\). Thus, we can factor it as:
\[
x^2 - 2x - 8 = (x - 4)(x + 2)
\]

Therefore, the numerator can be rewritten as:
\[
-10(x - 4)(x + 2)
\]

2. **Rewrite the expression**: The original expression can be rewritten now:
\[
\frac{-10(x - 4)(x + 2)}{x + 2}
\]

3. **Cancel out the common term**: Since there's a common factor of \((x + 2)\) in both the numerator and the denominator, we can cancel it out (as long as \(x \neq -2\)):
\[
-10(x - 4)
\]

4. **Distribute**: Finally, distribute \(-10\):
\[
-10x + 40
\]

Thus, the simplified expression for \(-10x^2 + 20x + 80\) divided by \(x + 2\) is:

\[
-10x + 40
\]

From the given options, the answer is:

**c. -10x + 40**.