Factor the GCF out of the polynomial: -20x^5 -4x^3 -4x^2

To factor the Greatest Common Factor (GCF) out of the polynomial \(-20x^5 - 4x^3 - 4x^2\), follow these steps:

1. **Identify the GCF of the coefficients**:
   - The coefficients are \(-20\), \(-4\), and \(-4\).
   - The GCF of these numbers is \(4\).

2. **Identify the GCF of the variables**:
   - The terms contain \(x^5\), \(x^3\), and \(x^2\).
   - The GCF of these terms is \(x^2\) (the lowest power of \(x\) present in all terms).

3. **Combine the GCF of the coefficients and the variables**:
   - The overall GCF of the polynomial is \(4x^2\).

4. **Factor the GCF out of each term**:
   - Factor \(4x^2\) out of \(-20x^5\): \(-20x^5 \div 4x^2 = -5x^3\).
   - Factor \(4x^2\) out of \(-4x^3\): \(-4x^3 \div 4x^2 = -x\).
   - Factor \(4x^2\) out of \(-4x^2\): \(-4x^2 \div 4x^2 = -1\).

5. **Write the factored expression**:
   - The factored form of the polynomial is:
     \[
     -20x^5 - 4x^3 - 4x^2 = 4x^2(-5x^3 - x - 1)
     \]

So, the final factored expression is:

\[
4x^2(-5x^3 - x - 1)
\]

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

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Here are 5 related questions:

1. How do you factor the GCF from a polynomial with more than three terms?
2. What is the next step after factoring the GCF if you need to factor the polynomial completely?
3. How do you factor polynomials where the GCF includes both a variable and a constant?
4. What happens if the GCF is negative, and how does it affect the factored expression?
5. Can you factor out the GCF from a polynomial if there is no common factor among all terms?

**Tip:** Always check each term to ensure you’ve factored out the correct GCF by multiplying the factor back through the parentheses.

Learn how to factor the Greatest Common Factor (GCF) from the polynomial -20x^5 - 4x^3 - 4x^2. This problem involves identifying the GCF of coefficients and variables, and factoring it out step-by-step. Suitable for high school students learning polynomial factoring.

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