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
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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