Factoring shows up everywhere on the SAT — from solving equations to simplifying expressions. Here are all the methods you need, ranked from most to least common.

Method 1: Greatest Common Factor (GCF)

Always check for a GCF first.

Example 1: Factor

Method 2: Factoring

Find two numbers that multiply to and add to .

Example 2: Factor

We need two numbers that multiply to 12 and add to 7. Those are 3 and 4.

Example 3: Factor

Multiply to , add to : that's and .

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Method 3: Factoring (a ≠ 1)

Use the AC method:

  1. Multiply
  2. Find two numbers that multiply to and add to
  3. Rewrite the middle term and factor by grouping

Example 4: Factor

. Numbers that multiply to 6 and add to 7: and .



Method 4: Difference of Squares

Example 5: Factor

Example 6: Factor

Method 5: Perfect Square Trinomials


Example 7: Factor

Check: the middle term . ✓

Connecting Factoring to Solving Equations

Once factored, set each factor equal to zero.

Example 8: Solve


Practice Problems

Problem 1: Factor

Solution

Multiply to 20, add to : and .

Problem 2: Factor

Solution

GCF first:

Problem 3: Solve

Solution

, numbers: and

or

Key Takeaways

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