Factoring Monomials

Definition: Factoring a monomial involves writing it as a product of its prime factors. Also known as prime factorization, this can be expressed using prime numbers, single variables and sometimes -1.

Example: Factor the following monomial: 54x³y²z

Solution: 

Step 1: Start by finding the prime factorization of 54, which can be written as 3 * 3 * 3 * 2

Step 2: Break the exponents down into expanded form:

x³ = x * x * x
y² = y * y

Step 3: Combine all factors into one expression. Note that z cannot be factored further:

3 * 3 * 3 * 2 * x * x * x * y * y * z

Step 4: Multiply to check your answer:

3 * 3 * 3 * 2 * x * x * x * y * y * z = 54x³y²z

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