What is the greatest common factor of the following sets of monomials?
$6x,9x^2,15x^3$

• A. $x$
• B. $3x$
• C. $15x$
• D. $x^3$

Answer: (B)

Verified step by step guidance

1. Identify the terms given in the problem. Since the problem is about finding the GCF (Greatest Common Factor) of terms, list all the terms you need to analyze.
2. Find the prime factorization of each term. Break down each number or algebraic term into its prime factors or variable factors with their exponents.
3. Compare the prime factorizations of all terms to determine the common factors. Look for the factors that appear in every term.
4. For each common factor, take the smallest exponent that appears in all terms. This ensures the factor divides all terms.
5. Multiply these common factors together to write the GCF. Express the GCF in its simplest form, combining numbers and variables as appropriate.