Factoring Monomials Worksheets

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: $$6^2\cdot x\cdot y\cdot z^3$$
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