Factor by grouping
Sometimes the terms of a polynomial have a greatest common factor of 1, but it still may be possible to factor the polynomial by using a process called factoring by grouping. We usually
factor by grouping when a polynomial has more than three terms.
For example, to factor the polynomial
ax – ay + bx – by,
Group the terns as follows.
(ax – by) + (bx – by)
Then factor ax – ay as a(x – y) and factor bx – by as b(x – y).
ax – ay + bx – by = (ax – ay) + (bx – by)
= a(x – y) + b(x – y)
The common factor is x – y. The final factored from is
ax – ay + bx – by = (x – y) (a + b).