WEBVTT 00:00:00.270 --> 00:00:04.040 These are the correct factors for each part of the fractions. I know factoring 00:00:04.040 --> 00:00:07.592 can be tough, so if you're getting at least half of these right, great work. If 00:00:07.592 --> 00:00:11.313 you got stuck on one of these, try to look back at your work and see where you 00:00:11.313 --> 00:00:15.305 went wrong to get these factors. If you can't find an error in your work then 00:00:15.305 --> 00:00:19.500 stay with me for this solution. For our first numerator we can pull out a 2x 00:00:19.500 --> 00:00:25.190 from each term. So we'll have 2x times x squared minus 6x plus 9. Then we notice 00:00:25.190 --> 00:00:29.626 that this is a special factoring pattern. It's a perfect square trinomial. So we 00:00:29.626 --> 00:00:35.557 have 2x times x minus 3, times x minus 3. This gives us our first numerator. For 00:00:35.557 --> 00:00:40.117 this denominator, we want to find the factors of negative 12, that sum to 00:00:40.117 --> 00:00:44.063 negative 4. This allows us to rewrite our middle term. And then we'll use 00:00:44.063 --> 00:00:48.581 factoring by grouping to get 3x plus 2 times x minus 2. This is our factored 00:00:48.581 --> 00:00:53.356 form for our first denominator. For this numerator we want to find the factors 00:00:53.356 --> 00:00:58.442 of 12 that sum to negative 8. These two factors are negative 6, 6 and negative 00:00:58.442 --> 00:01:03.928 2. We'll use factoring by grouping to get 3x minus 2 time x minus 2 for this 00:01:03.928 --> 00:01:09.403 numerator. And finally for this last denominator we pull out a 6x from both 00:01:09.403 --> 00:01:14.363 terms leaving us with 6x times x squared minus 9. Then we can factor this 00:01:14.363 --> 00:01:18.771 difference of squares using x plus 3 times x minus 3. This difference of squares 00:01:18.771 --> 00:01:22.754 pattern appears in all sorts of math. So it's great that we can recognize it 00:01:22.754 --> 00:01:23.360 quickly.