https://file.aiquickdraw.com/mathbot/file/17268536173919zmbtcls.jpg

Let's analyze the problem.

The given function is:

\[
f(x) = \frac{3x^2 - 5x - 2}{x^2 + 2x - 8}
\]

### Step 1: Factor both the numerator and the denominator
We begin by factoring the denominator and numerator to check for discontinuities.

#### Denominator:
\[
x^2 + 2x - 8 = (x - 2)(x + 4)
\]
This gives two potential discontinuities at \( x = 2 \) and \( x = -4 \).

#### Numerator:
\[
3x^2 - 5x - 2 = (3x + 1)(x - 2)
\]
The factor \( (x - 2) \) appears in both the numerator and denominator.

### Step 2: Simplifying the function
The common factor of \( (x - 2) \) in both the numerator and denominator cancels out, but it still indicates a removable discontinuity at \( x = 2 \).

After canceling \( (x - 2) \), the simplified function becomes:

\[
f(x) = \frac{3x + 1}{x + 4}
\]

### Step 3: Non-removable discontinuities
The remaining denominator \( x + 4 \) shows that \( x = -4 \) is a non-removable discontinuity because it causes the denominator to be zero, which makes the function undefined at that point.

### Conclusion:
- At \( x = 2 \), there is a removable discontinuity.
- At \( x = -4 \), there is a non-removable discontinuity.

Thus, the correct answer is **(B) \( -4 \) only**, which matches the boxed answer in the image.

Would you like more details or have any questions about this solution?

Here are 5 related questions to explore:
1. What is the difference between removable and non-removable discontinuities?
2. How does canceling a factor affect the type of discontinuity?
3. Can a function have more than one removable discontinuity?
4. What are some examples of functions with both types of discontinuities?
5. How do you determine if a discontinuity is removable or non-removable from a graph?

**Tip:** Always factor both the numerator and denominator of a rational function to identify potential discontinuities.

Let f be the function given by f(x) = (3x^2 - 5x - 2) / (x^2 + 2x - 8). For what values of x does f have a non-removable discontinuity?

Explore how to find non-removable discontinuities for the function f(x) = (3x^2 - 5x - 2) / (x^2 + 2x - 8). This step-by-step guide covers factoring quadratics and identifying discontinuities, suitable for high school students.

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