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Definition of Factoring

In arithmetic, factoring (or factorization) means finding combinations of integers that multiply together to give the integer being factored. In algebra, factoring polynomials means finding polynomials of lower order (lower variable exponent) that, multiplied together, equal the polynomial being factored.

  1. Factoring a Number

    • Full factorization of an integer means finding all the primes that divide evenly into an integer. For example, 24 = (2^3)---3. Two and three are called "factors" and 24 is called a "multiple" of two and three.

    Greatest Common Factor

    • Greatest Common Factor is 4

      When simplifying a fraction, one divides out the greatest common factor of the numerator and denominator. This is not to be confused with the least common multiple, which is used when combining fractions with different denominators.

    Factoring in Algebra

    • In algebra, unknown numbers are represented with letters and called "variables." An example of factoring with variables is breaking xy+3y into y---(x+3). Because of the use of x as a variable, the similar-looking multiplication sign is avoided: y(x+3).

    Factoring By Grouping

    • Factoring by Grouping

      Sometimes four terms can be factored into two. For example, 2x^2+10x+3x+15 = 2x(x+5) + 3(x+5).

    Trinomials

    • Trinomial Factorization

      A polynomial is a formula of variables added together. Factoring by grouping can be used for trinomials (three-term polynomials). For ax^2+bx+c, find factors of b that sum to the product ac. Then the formula can be rewritten in four terms and factoring by grouping can be performed.

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