[Script Info]
Title:
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.18,0:00:04.15,Default,,0000,0000,0000,,We want to start by looking for our Greatest Common Factor and what do you know
Dialogue: 0,0:00:04.15,0:00:08.45,Default,,0000,0000,0000,,all the coefficients are even, so 2 can come out. Now that we factored out a 2,
Dialogue: 0,0:00:08.45,0:00:13.34,Default,,0000,0000,0000,,we want to continue factoring this inside portion if possible. We want to find
Dialogue: 0,0:00:13.34,0:00:18.72,Default,,0000,0000,0000,,factors of positive 14 and some to negative 15. This 14 comes from multiplying
Dialogue: 0,0:00:18.72,0:00:23.86,Default,,0000,0000,0000,,the coefficient of the x squared term 2 by the constant term 7. The negative 15
Dialogue: 0,0:00:23.86,0:00:28.100,Default,,0000,0000,0000,,is simply the coefficient of our x term. We have a positive 14 and a negative
Dialogue: 0,0:00:28.100,0:00:33.69,Default,,0000,0000,0000,,15. This must mean every factor in a factor pair must be negative. We want to
Dialogue: 0,0:00:33.69,0:00:38.73,Default,,0000,0000,0000,,use negative 1 and negative 14 since they multiply to give us positive 14 and
Dialogue: 0,0:00:38.73,0:00:43.25,Default,,0000,0000,0000,,they add to negative 15. We continue factoring this portion by rewriting the
Dialogue: 0,0:00:43.25,0:00:47.43,Default,,0000,0000,0000,,middle term with these two factors as coefficients for x. Then we factor by
Dialogue: 0,0:00:47.43,0:00:51.50,Default,,0000,0000,0000,,grouping. We take out an x from the first two terms and a negative 7 from the
Dialogue: 0,0:00:51.50,0:00:56.08,Default,,0000,0000,0000,,second two terms. When I remove a negative 7 from positive 7, I'm left with
Dialogue: 0,0:00:56.08,0:01:01.45,Default,,0000,0000,0000,,negative 1 here. I also know I did this step correctly, since negative 7 times
Dialogue: 0,0:01:01.45,0:01:06.66,Default,,0000,0000,0000,,2x is negative 14x. And negative 7 times negative 1 is positive 7. We have a
Dialogue: 0,0:01:06.66,0:01:11.56,Default,,0000,0000,0000,,common factor of 2x minus 1. So this is our completed factor form. Fantastic
Dialogue: 0,0:01:11.56,0:01:13.51,Default,,0000,0000,0000,,work, if you got that correct.