To factor the expression \(-\frac{1}{4}x^2 - 4x - 12\), follow these steps:

### 1. Factor out the negative sign:
\[
-\left(\frac{1}{4}x^2 + 4x + 12\right)
\]

### 2. Eliminate the fraction by factoring out \(\frac{1}{4}\) from the remaining expression:
\[
-\frac{1}{4}\left(x^2 + 16x + 48\right)
\]

### 3. Now factor the quadratic expression inside the parentheses:
We need two numbers that multiply to 48 and add to 16. These numbers are 12 and 4.

\[
x^2 + 16x + 48 = (x + 12)(x + 4)
\]

### 4. Substitute the factorized form back into the expression:
\[
-\frac{1}{4}(x + 12)(x + 4)
\]

Thus, the fully factored form is:
\[
-\frac{1}{4}(x + 12)(x + 4)
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you factor quadratic expressions in general?
2. What is the importance of factoring out common terms?
3. How do you deal with negative leading coefficients when factoring?
4. What methods can be used to factor trinomials efficiently?
5. How does factoring relate to finding the roots of an equation?

**Tip**: Always check if you can factor out a common constant to simplify factoring polynomials.

Learn how to factor the quadratic expression -1/4x²-4x-12 with a detailed, step-by-step breakdown. This solution includes factoring out constants, simplifying fractions, and identifying factors of quadratic trinomials. Suitable for Grades 9-11 students.

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