# 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.

## References

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