When factoring a trinomial by grouping, why is it necessary to write the trinomial in four terms? Provide an example. Thank you.
It is necessary to write four terms in order to group the first and second sets of expressions so that
the binomial factors of the trinomial can be identified. For example:
can be factored easily by REPLACING - 7x with - 15x and 8x.
Thus, becomes . The first two expressions: as well as the last
two: can now be factored, thus eliminating the "trial and error" method, associated with the leading
coefficient, 24 having 4 sets of factors:
1 & 24
2 & 12
3 & 8, and
4 & 6
After writing the above trinomial in four terms, it was determined that the factors of 24 to be used are: 3 & 8,
as the trinomial factors to: 3x(8x - 5) + 1(8x - 5), leading to the trinomial's factors being: