We want to start by looking for our Greatest Common Factor and what do you know
all the coefficients are even, so 2 can come out. Now that we factored out a 2,
we want to continue factoring this inside portion if possible. We want to find
factors of positive 14 and some to negative 15. This 14 comes from multiplying
the coefficient of the x squared term 2 by the constant term 7. The negative 15
is simply the coefficient of our x term. We have a positive 14 and a negative
15. This must mean every factor in a factor pair must be negative. We want to
use negative 1 and negative 14 since they multiply to give us positive 14 and
they add to negative 15. We continue factoring this portion by rewriting the
middle term with these two factors as coefficients for x. Then we factor by
grouping. We take out an x from the first two terms and a negative 7 from the
second two terms. When I remove a negative 7 from positive 7, I'm left with
negative 1 here. I also know I did this step correctly, since negative 7 times
2x is negative 14x. And negative 7 times negative 1 is positive 7. We have a
common factor of 2x minus 1. So this is our completed factor form. Fantastic
work, if you got that correct.