Polynomials & Factoring
Look for a common factor, then a pattern.
The rules
- Always pull out the greatest common factor first.
- Difference of squares: a² − b² = (a − b)(a + b).
- Perfect-square trinomial: a² + 2ab + b² = (a + b)².
- To factor x² + bx + c, find two numbers that multiply to c and add to b.
Watch out: Missing a common factor before using a pattern.
Worked example
Factor x² − 49.
- This is a difference of squares.
- x² − 7² = (x − 7)(x + 7).
Answer: (x − 7)(x + 7)
Try it yourself
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