Factor by Grouping
Factor by Grouping
Factoring
When a polynomial is written as the product of two or more polynomials, the polynomial has been factored. Here is an example:
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.