Question

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

Answer 1

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

First, we set the denominator to zero:

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

To simplify this, we can factor out \(-2\):

\[
-2(x^2 + 8x + 16) = 0
\]

Now, we solve the quadratic equation:

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

This can be factored as:

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

or

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

Setting the factor equal to zero gives us:

\[
x + 4 = 0 \quad \Rightarrow \quad x = -4
\]

Thus, the value that would cause the rational expression to be undefined is:

\[
\boxed{-4}
\]