# Factoring Monomials

- - Pre-Algebra

Factoring 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.

Examples:

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

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

B. Write the prime-power factorization of each.

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