Factor by Grouping

x³ - 3x² - 2x +6 = (x - 3)(x² - 2)

The polynomials (x - 3) and (x² - 2) are called factors of the polynomial. Note that the degrees of the factors, 1 and 2, respectively, add up to the degree of the original polynomial. Thus factoring breaks up a complicated polynomial into lower degree pieces. In this case, one of the factors can be factored further:

(x - 3)(x² - 2) = (x - 3) (x + )(x - )

Now that the polynomial has been factored into three linear or degree 1 polynomials, the polynomial cannot be factored any farther. Therefore, this polynomial has been factored completely.