Question

What value would cause the rational expression 5x + 15/−2x^2−16x − 32
to be undefined?(1 point)
Responses

2
2

-4
-4

4
4

-2

Answer 1

To determine when the rational expression \(\frac{5x + 15}{-2x^2 - 16x - 32}\) is undefined, we need to find when the denominator equals zero.

First, we set the denominator equal to zero:

\[
-2x^2 - 16x - 32 = 0
\]

To simplify this, we can divide the entire equation by -2:

\[
x^2 + 8x + 16 = 0
\]

Now we can factor this quadratic equation:

\[
(x + 4)(x + 4) = 0
\]

This can be written as:

\[
(x + 4)^2 = 0
\]

Thus, the solution is:

\[
x + 4 = 0 \implies x = -4
\]

Therefore, the value that causes the rational expression to be undefined is \(-4\).

**Answer: -4**