Types of Factoring

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The central idea of all factoring is to rewrite a mathematical object as a product. In arithmetic, factoring is rewriting an integer as the product of its component numbers, especially into prime integers. In algebra, factoring is the rewriting of a polynomial as a product of polynomials of lower order (lower variable exponent).

Factoring Out a Common Factor

  • In simplifying a fraction, one finds the common factor in the numerator and denominator of the fraction.

Factoring by Grouping

  • A factoring problem with four terms often is a grouping problem. The method is to factor in two stages.

Factoring a Trinomial

  • A trinomial of form ax^2+bx+c can be factored by finding factors of the product ac that sum to b.

Factoring Perfect Squares

  • If a and c are squared integers, the trinomial can be a perfect square.

Factoring the Difference of Two Squares

  • The difference of two squares a-squared + b-squared always factors into the product the sum and difference of a and b.

Factoring the Sum or Difference of Two Cubes

  • There are simple formulas for factoring the sum or difference of two cubes that can be verified by multiplying out the factors.

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