Greatest Common Factor Method

Determine the greatest common factor of the polynomial. This can be absolutely anything every term has in common. For instance, the polynomial 5xy+35y+10y2 has the factor 5y in common. Another example is 5(x+y) – 2x(x+y). This polynomial has (x+y) in common.

Divide out the greatest common factor. In the above examples, you would have 5y(x+7+2y) and (x+y)(5-2x).

Check the factors by multiplying them back out. If you reach the original polynomial, then your factors are correct.

Grouping Method

Group terms together if you have four terms without a greatest common factor.

Group the first two terms together and the last two terms together. For instance, x3+5x2+2x+10 would be grouped as (x3+5x2)+(2x+10).

Find the greatest common factor for each group. (x3+5x2)+(2x+4) would become x2(x+5)+2(x+5).

Factor out the common binomial. In this case that would be (x+5).

Combine the outer terms into their own factor: (x2+2)(x+5).

Check the factors by multiplying them back out. If you reach the original polynomial, then your factors are correct.

Tips

• Some polynomials cannot be factored using the greatest common factor. These will require synthetic division and sometimes will still not be able to be factored.