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, first write down all the terms clearly.
2. Factor each term into its prime factors, including both numerical coefficients and variables with their exponents. For example, if a term is \$12x^3y$, factor it as \(2 \times 2 \times 3 \times x^3 \times y\).
3. List the common factors that appear in all terms. This includes the prime numbers and variables with the smallest exponent that appear in every term.
4. Multiply all the common factors together to form the GCF. For variables, use the lowest power of each variable that appears in all terms.
5. Write the GCF as the product of these common factors. This expression represents the greatest factor that divides all the given terms.