Question

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

Answer 1

The rational expression \( \frac{5x + 15}{-2x^2 - 16x - 32} \) is undefined when the denominator is equal to zero.

To find the value(s) of \( x \) that cause the expression to be undefined, we need to set the denominator equal to zero and solve for \( x \):

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

Dividing each term by -2 gives:

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

Now, we can factor the quadratic expression:

\[
(x + 4)(x + 4) = 0 \quad \text{or} \quad (x + 4)^2 = 0
\]

Setting the factor equal to zero gives us:

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

Thus, the rational expression is undefined at \( x = -4 \).

So the answer is:

\[
x = -4
\]