1Cademy - Factoring $$12x

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Factoring the Greatest Common Factor from a Polynomial

Example

Factoring $12x - 60$

Factor $12x - 60$ by extracting the greatest common factor.

Step 1 — Find the GCF of $12x$ and $60$ : Write out the prime factors of each term: $12x = 2 \cdot 2 \cdot 3 \cdot x$ and $60 = 2 \cdot 2 \cdot 3 \cdot 5$ . The factors common to both are $2, 2,$ and $3$ , so $\text{GCF} = 2 \cdot 2 \cdot 3 = 12$ .

Step 2 — Rewrite each term as a product of the GCF: Express $12x = 12 \cdot x$ and $60 = 12 \cdot 5$ , giving $12 \cdot x - 12 \cdot 5$ .

Step 3 — Factor out the GCF using the reverse Distributive Property: $12(x - 5)$ .

Step 4 — Check by multiplying: $12(x - 5) = 12 \cdot x - 12 \cdot 5 = 12x - 60$ ✓.

The factored form is $12(x - 5)$ . This example demonstrates factoring when the GCF is a larger number ( $12$ ) that requires prime factorization to identify, rather than being immediately obvious from inspection.

Updated 2026-04-21

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OpenStax Elementary Algebra

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