How Do You Factor Polynomials With Four Terms?

A four-term polynomial is most often factored by grouping, a process where terms that have common factors are grouped and factored separately. In some cases, separate factoring of the two groups may reveal another factor common to both groups.

  1. Separate the terms of the polynomial into two groups

    For example, consider the polynomial x^3 + 5x^2 + 3x + 15. No terms can be combined because each term has a different degree of x, but grouping terms allows factoring. In this case, the first two terms share a common factor of x^2, and the last two terms have a common factor of 3, so rewrite the polynomial as (x^3 + 5x^2) + (3x + 15).

  2. Factor each binomial separately

    The term x^2 can be factored from (x^3 + 5x^2), resulting in the new term: x^2(x + 5). The number 3 can be factored from (3x + 15), resulting in the new term 3(x + 5).

  3. Combine any like terms

    The factored polynomial is x^2(x + 5) + 3(x + 5). In this case, the polynomial can be factored further by combining the term (x + 5), which is a factor in both terms: x^2(x + 5) + 3(x + 5) = (x + 5)(x^2 + 3).