- If necessary, put the polynomial in standard form.
- If possible, pull out any factors common to all terms (§6.1).
- If there are four terms, try factoring by grouping (§6.1).
- If there are three terms, try factoring into two binomials (§§6.2&6.3) or factoring as a perfect square (§6.4).
- If there are two terms (or if you now have factors with two terms), try factoring as a sum or difference of squares or cubes (§6.4).
- Keep factoring the factors until you can factor no further (§6.5).

For definiteness, here are the conditions that must be met for a polynomial (with rational coefficients) to be completely factored:

- The first factor must be a constant, except that (unless it is the only factor) we leave it out if it is 1 or use just a minus sign if it is −1.
- Every other factor must be a non-constant polynomial with integer coefficients and a positive leading coefficient.
- No factor's coefficients may have a common integer factor greater than 1.
- No factor may be a product of two non-constant polynomials.

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