- Ch. 0What Is Factorization?Write a polynomial as a product, like 60 = 2×2×3×5, until nothing splits.
- Ch. 1Taking Out a Common FactorTake out what every term shares, all at once, and keep the 1s in the bracket.
- Ch. 2Using the FormulasSquares and cubes, sums and differences: each formula is a picture to cut up.
- Ch. 3Factoring by GroupingNo common factor overall? Group the terms so that the brackets match.
- Ch. 4Splitting and Adding TermsOne term short of a formula? Add it and subtract it. Same value, open road.
- Ch. 5The Cross MethodSplit the constant so that the cross products add up to the middle term.
- Ch. 6Quadratics in Two VariablesTwo letters, six terms. Use three columns, and all three crosses must match.
- Ch. 7Putting It All TogetherYou know the tools; the hard part is which one first. Ask in a fixed order.
- Ch. 8Linear Factors of a PolynomialIf f(c) = 0, then (x − c) is a factor, and only a few rationals are worth a try.
- Ch. 9The Method of Undetermined CoefficientsGuess the shape of the factors with letters, multiply out, match, and solve.
- Ch. 10Cyclic and Symmetric ExpressionsLetters swap seats but the expression stays put. One factor gives you the rest.
- Ch. 11Factoring over the Reals and the Complex Numbers“Cannot be split” depends on the numbers allowed. More numbers, finer factors.
- Ch. 12Irreducible PolynomialsHow can you be sure nothing splits? Eisenstein's criterion uses a prime.