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.
- 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).
- 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).
- 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).