Answer :
Final answer:
The greatest common factor for 30x^(2) and 45x^(5) is 15x^(2).
Explanation:
To find the greatest common factor (GCF) for 30x^(2) and 45x^(5), we need to break down each term into its prime factors.
For 30x^(2), we can break it down as:
- 30 = 2 * 3 * 5
- x^(2) = x * x
For 45x^(5), we can break it down as:
- 45 = 3 * 3 * 5
- x^(5) = x * x * x * x * x
Now, let's identify the common factors:
- Both terms have a factor of 3 and 5.
- For the variable x, the first term has x^(2) and the second term has x^(5). The highest power of x that appears in both terms is x^(2).
Therefore, the greatest common factor for 30x^(2) and 45x^(5) is 3 * 5 * x^(2), which can be simplified as 15x^(2).
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