Question 895587
When factoring a trinomial by grouping, why is it necessary to write the trinomial in four terms? Provide an example. Thank you.
<pre>
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:
{{{24x^2 - 7x - 5}}} can be factored easily by REPLACING - 7x with - 15x and 8x.

Thus, {{{24x^2 - 7x - 5}}} becomes {{{24x^2 - 15x + 8x - 5}}}. The first two expressions: {{{24x^2 - 15x}}} as well as the last
two: {{{+ 8x - 5}}} 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: {{{highlight_green((3x + 1)(8x - 5))}}}