1Cademy - Factoring $$4x + 12$$

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Factoring

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Factoring $4x + 12$

Factor $4x + 12$ by extracting the greatest common factor.

Step 1 — Find the GCF of $4x$ and $12$ : Factor each term into primes: $4x = 2 \cdot 2 \cdot x$ and $12 = 2 \cdot 2 \cdot 3$ . The common factors are two $2$ s, so $\text{GCF} = 2 \cdot 2 = 4$ .

Step 2 — Rewrite each term as a product of the GCF: Express $4x = 4 \cdot x$ and $12 = 4 \cdot 3$ , giving $4 \cdot x + 4 \cdot 3$ .

Step 3 — Apply the reverse Distributive Property: Factor out the $4$ : $4(x + 3)$ .

Step 4 — Check by multiplying: $4(x + 3) = 4 \cdot x + 4 \cdot 3 = 4x + 12$ ✓.

The factored form is $4(x + 3)$ .

Updated 2026-04-21

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OpenStax Elementary Algebra

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Elementary Algebra @ OpenStax

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