WEBVTT 00:00:00.220 --> 00:00:04.157 You might be wondering where the 30 and the 11 come from in the number puzzle. 00:00:04.158 --> 00:00:08.726 Well we actually multiply the coefficient of the x squared term and the constant 00:00:08.726 --> 00:00:13.111 term together to get this top number. This bottom number 11 comes from our x 00:00:13.111 --> 00:00:17.668 term. Whenever we want to factor a trinomial we can set up a number puzzle and 00:00:17.668 --> 00:00:23.038 then find the two factors we need to rewrite the x term. So, I can rewrite this 00:00:23.038 --> 00:00:30.014 expression as x squared plus 5x plus 6x plus 30. We can rewrite the 11x as 5x 00:00:30.014 --> 00:00:36.094 and 6x. The 2 numbers come from our number puzzle. By rewriting this x term as 00:00:36.094 --> 00:00:41.496 5x plus 6x we can use factoring by grouping. I remove an x from the first 2 00:00:41.496 --> 00:00:46.850 terms and a six from the second two terms. And whoa, look at that, our factored 00:00:46.850 --> 00:00:52.188 form. So for any quadratic trinomial, we can try this process to factor it. We 00:00:52.188 --> 00:00:57.280 can find two factors of a times c, that sum to the middle number b. We'll 00:00:57.280 --> 00:01:02.033 rewrite the middle term using those factors and then try factoring by grouping.