Factor by grouping

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).


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