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Let's analyze the polynomial:

\[
-16a^4 + 12a^3 - 4a^2
\]

The task is to factor out a negative number or the greatest common factor (GCF) that has a negative coefficient.

### Step 1: Identify the GCF
The coefficients are \(-16\), \(12\), and \(-4\). The GCF of these numbers is 4. However, since we are asked to factor out a **negative** number, we'll factor out \(-4\).

### Step 2: Factor out \(-4\)
Factoring \(-4\) from each term:
\[
-4(4a^4 - 3a^3 + a^2)
\]

### Step 3: Verify the factored form
Distribute \(-4\) back into the expression to check:
\[
-4(4a^4 - 3a^3 + a^2) = -16a^4 + 12a^3 - 4a^2
\]
This confirms the factorization is correct.

The final factored form is:

\[
-4(4a^4 - 3a^3 + a^2)
\]

Would you like further details or clarifications on this?

Here are 5 related questions you might consider:
1. How do you determine the GCF of terms in a polynomial?
2. What is the process of factoring polynomials with higher degrees?
3. How would the factoring change if the polynomial had more terms?
4. Can you use synthetic division to factor polynomials?
5. How can you verify the factored form of a polynomial?

**Tip:** Always double-check your factoring by multiplying the factors back together to ensure they produce the original expression.

Factor a negative number or a GCF with a negative coefficient from the polynomial: -16a^4 + 12a^3 - 4a^2

Learn how to factor the polynomial -16a^4 + 12a^3 - 4a^2 by factoring out the greatest common factor (GCF) with a negative coefficient. This detailed step-by-step solution explores polynomial factoring and algebra concepts, suitable for students in Grades 9-12.

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