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Answer :
Final answer:
The greatest common factor of 35x^4, 21x^5, and 3x^3 is x^3.
Explanation:
To find the greatest common factor (GCF) of the three expressions 35x4, 21x5, and 3x3, we need to factorize each expression and find the highest power of each factor that appears in all three expressions.
The prime factorization of 35x4 is 5 * 7 * x * x * x * x, the prime factorization of 21x5 is 3 * 7 * x * x * x * x * x, and the prime factorization of 3x3 is 3 * x * x * x.
Looking at the factorization, the highest power of 5 that appears in all three expressions is 0 (since 5 only appears in the first expression), the highest power of 7 that appears is 0 (since 7 only appears in the first and second expressions), and the highest power of x is 3 (since x appears with power 4, 5, and 3). Therefore, the GCF is 50 * 70 * x3 = x3.
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