factor out the common factor of $$ 24r-60r^2+60r^6 $$

To factor out the greatest common factor (GCF) from the expression $ 24r - 60r^2 + 60r^6 $, follow these steps:

1. **Identify the GCF of the coefficients**:  
   - The coefficients are 24, 60, and 60.
   - The GCF of 24, 60, and 60 is 12.

2. **Identify the GCF of the variable terms**:  
   - The variable terms are $ r $, $ r^2 $, and $ r^6 $.
   - The GCF of $ r $, $ r^2 $, and $ r^6 $ is $ r $ (the smallest power of $ r $).

3. **Combine the GCFs**:
   - The overall GCF is $ 12r $.

4. **Factor out the GCF from the expression**:
   - $ 24r - 60r^2 + 60r^6 = 12r(2 - 5r + 5r^5) $.

So, the factored expression is:
\[
\boxed{12r(2 - 5r + 5r^5)}
\]

Would you like more details or have any questions? Here are five related questions you might find interesting:

1. How do you factor out the GCF from a polynomial with more than three terms?
2. What are the steps to factor completely after factoring out the GCF?
3. How do you factor an expression like $ 60r^6 - 24r^4 + 36r^2 $?
4. What is the difference between factoring out the GCF and factoring by grouping?
5. Can you factor the expression $ 12r^3 + 18r^2 - 24r $ completely?

**Tip:** After factoring out the GCF, always check if the remaining expression can be factored further.

Learn how to factor out the greatest common factor (GCF) from the polynomial expression 24r - 60r^2 + 60r^6 step-by-step. This problem involves polynomials and factoring techniques, specifically focusing on identifying and factoring out the GCF. Suitable for high school students and beyond.

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