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: \(6^2\cdot x\cdot y\cdot z^3\)

WORKSHEETS: 

• Worksheet 1 (20 FREE RESPONSE items with answers)
• Worksheet 1 (20 MULTIPLE CHOICE items with answers)
• Worksheet 2 (30 FREE RESPONSE items with answers)
• Worksheet 2 (30 MULTIPLE CHOICE items with answers)
• Worksheet 3 (40 FREE RESPONSE items with answers)
• Worksheet 3 (40 MULTIPLE CHOICE items with answers)
• Worksheet 4 (50 FREE RESPONSE items with answers)
• Worksheet 4 (50 MULTIPLE CHOICE items with answers)

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