Factoring Monomials

- - Pre-Algebra

Factoring Monomials HeaderFactoring monomials is the same thing with factoring numbers. In our previous discussion of factoring, any integer can be written uniquely as a product of prime factors. Hence, the "prime factorization" of a monomial is writing its expression as a product of prime numbers, single variables, and (possibly) a –1.

On the other hand, the prime-power factorization of a monomial is writing its expression as a power of prime factors.


A. Write the prime factorization of each. Do not use exponents.

  1. 81x^2Answer: 3\cdot 3\cdot 3\cdot 3\cdot x\cdot x
  2. 14nAnswer: 2\cdot 7\cdot n
  3. 92xyAnswer: 2\cdot 2\cdot 23\cdot x\cdot y
  4. 8x^3yAnswer: 2\cdot 2\cdot 2\cdot x\cdot x\cdot x\cdot y
  5. 32r^2s^5Answer: 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot r\cdot r\cdot s\cdot s\cdot s\cdot s\cdot s

B. Write the prime-power factorization of each.

  1. 82abAnswer: 2\cdot 41\cdot a\cdot b
  2. 16x^5y^4z^3Answer: 2^4\cdot x^5\cdot y^4\cdot z^3
  3. 25xy^2Answer: 5^2\cdot x\cdot y^2
  4. 18x^8y^9Answer: 2\cdot 3^2\cdot x^8\cdot y^9
  5. 36xyz^3Answer: 6^2\cdot x\cdot y\cdot z^3

Factoring Monomials Worksheets

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