Factor the polynomial. $$ 24 c y-12 c x-12 a y+6 a x $$

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To factor the polynomial $$ 24c y - 12c x - 12a y + 6a x $$, follow these steps:

1. **Factor by Grouping:**
   Group the terms in pairs:
   $$
   (24c y - 12c x) + (-12a y + 6a x)
   $$

2. **Factor Out the Greatest Common Factor (GCF) from Each Group:**
   - From the first group $$24c y - 12c x$$, factor out $$12c$$:
     $$
     12c(2y - x)
     $$
   - From the second group $$-12a y + 6a x$$, factor out $$6a$$:
     $$
     6a(-2y + x) = -6a(2y - x)
     $$
   
3. **Combine the Factored Groups:**
   $$
   12c(2y - x) - 6a(2y - x)
   $$
   
4. **Factor Out the Common Binomial Factor $$(2y - x)$$:**
   $$
   (2y - x)(12c - 6a)
   $$
   
5. **Factor Out the Numerical GCF from the Remaining Terms:**
   $$
   (2y - x) \cdot 6(2c - a) = 6(2c - a)(2y - x)
   $$

**Final Factored Form:**
$$
6(2c - a)(2y - x)
$$

Answer: After factoring, the expression is 6 ( 2 c – a ) multiplied by (2 y – x). Thus,

6(2c−a)(2y−x)
The factored form of the polynomial is $$6(2c - a)(2y - x)$$.

Factor the polynomial.

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