Question

What value would cause the rational expression 5x+15−2x2−16x−32 to be undefined?(1 point)
x=

Answer 1

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

Let's set the denominator equal to zero:

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

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

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

Now, we can factor the quadratic:

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

This gives us:

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

So, \(x + 4 = 0\) gives us:

\[
x = -4
\]

Thus, the rational expression is undefined when:

\[
\boxed{-4}
\]