Question 110316
{{{3w^2+14w+8}}}

:
We need to find two factors of the form {{{aw+b}}} and {{{cw+d}}}.  Both of the signs are + because the signs are all + in the given trinomial. We need to choose a, b, c, and d with the following relationships:

{{{a*c=3}}}
{{{b*d=8}}}
{{{a*d+b*c=14}}}
:
Possibilities for a and c are 1 and 3.
Possibilities for b and d are 1 and 8 or 2 and 4.
:
let's try a = 3 and c = 1.  3 * 4 = 12 and 1 * 2 = 2, 12 + 2 = 14.
So, a = 3, b = 2, c = 1, and d = 4.
:
{{{(3w+2)(w+4)}}}
:
Check:
{{{3w^2+12w+2w+8}}}
{{{3w^2+14w+8}}}