Question

A polynomial has two terms. Check all of the factoring methods that should be considered.

common factor

difference of cubes

sum of cubes

difference of squares

perfect-square trinomial

factoring by grouping

Answer 1

Check these:

- common factor — Yes. Always check for a greatest common factor in a two-term polynomial.
- difference of cubes — Yes, if the two terms are a^3 − b^3 (or can be written that way).
- sum of cubes — Yes, if the two terms are a^3 + b^3.
- difference of squares — Yes, if the two terms are a^2 − b^2.
- perfect-square trinomial — No. This is a 3-term pattern, not applicable to a binomial.
- factoring by grouping — No. Grouping requires (at least) four terms to group; not applicable to a simple two-term polynomial.

(Also note: a^2 + b^2 does not factor over the reals, so "sum of squares" is not a real factoring method unless complex factors are allowed.)