Factor the polynomial.
36azminus18axminus12czplus6cx

To factor the polynomial \(36az - 18ax - 12cz + 6cx\), follow these steps:

1. **Group the terms**:  
   \[
   (36az - 18ax) - (12cz - 6cx)
   \]

2. **Factor out the greatest common factor (GCF) from each group**:
   - From the first group, \(36az - 18ax\), the GCF is \(18a\).
   - From the second group, \(-12cz + 6cx\), the GCF is \(-6c\).

   So, the expression becomes:
   \[
   18a(2z - x) - 6c(2z - x)
   \]

3. **Factor out the common binomial factor**:  
   The common binomial factor is \((2z - x)\). Therefore, the factored form is:
   \[
   (18a - 6c)(2z - x)
   \]

4. **Simplify the coefficients**:
   - Notice that \(18a - 6c\) can be factored further. The GCF here is \(6\).
   - Factor out the \(6\), and you get:
   \[
   6(3a - c)(2z - x)
   \]

So, the fully factored form of the polynomial is:

\[
6(3a - c)(2z - x)
\]

Would you like further details or have any questions?

Here are 5 related questions to explore:

1. How do you determine the greatest common factor in a polynomial?
2. What are the steps to factor a polynomial completely?
3. Can you factor a polynomial with more than four terms?
4. How do you factor a polynomial with no common factors?
5. What is the role of grouping in factoring polynomials?

**Tip:** Always check if the factored terms can be simplified further. Simplification is key to arriving at the final, fully factored expression.

Learn how to factor the polynomial 36az - 18ax - 12cz + 6cx with detailed step-by-step instructions. This problem involves polynomial factoring techniques, including grouping and factoring out the greatest common factor (GCF). Suitable for high school students studying polynomials and algebra.

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