Factoring by Grouping: Four Terms
Certain polynomials with four terms can be factored using a method called factoring by grouping.
Consider the four-term polynomial
x3 + x2 + 2x + 2.
There is no factor other than 1 that is common to all the terms. We can, however, factor x3 + x2 and 2x + 2 separately:
x3 + x2 = x2 (x + 1); Factoring x3 + x2
2x + 2 = 2(x + 1) . Factoring 2x + 2
We have grouped certain terms and factored each polynomial separately:
x3 + x2 + 2x + 2 = (x3 + x2) + (2x + 2)
=x2(x + 1) + 2(x + 1)
=(x2 + 2)(x + 1)
This method is called factoring by grouping.We began with a polynomial with four terms. After grouping and removing common factors, we obtained a polynomial with two parts, each having a common factor Not all polynomials with four terms can be factored by this procedure, but it does give us a method to try.