﻿[Script Info] Title: [Events] Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text Dialogue: 0,0:00:00.22,0:00:04.16,Default,,0000,0000,0000,,You might be wondering where the 30 and the 11 come from in the number puzzle. Dialogue: 0,0:00:04.16,0:00:08.73,Default,,0000,0000,0000,,Well we actually multiply the coefficient of the x squared term and the constant Dialogue: 0,0:00:08.73,0:00:13.11,Default,,0000,0000,0000,,term together to get this top number. This bottom number 11 comes from our x Dialogue: 0,0:00:13.11,0:00:17.67,Default,,0000,0000,0000,,term. Whenever we want to factor a trinomial we can set up a number puzzle and Dialogue: 0,0:00:17.67,0:00:23.04,Default,,0000,0000,0000,,then find the two factors we need to rewrite the x term. So, I can rewrite this Dialogue: 0,0:00:23.04,0:00:30.01,Default,,0000,0000,0000,,expression as x squared plus 5x plus 6x plus 30. We can rewrite the 11x as 5x Dialogue: 0,0:00:30.01,0:00:36.09,Default,,0000,0000,0000,,and 6x. The 2 numbers come from our number puzzle. By rewriting this x term as Dialogue: 0,0:00:36.09,0:00:41.50,Default,,0000,0000,0000,,5x plus 6x we can use factoring by grouping. I remove an x from the first 2 Dialogue: 0,0:00:41.50,0:00:46.85,Default,,0000,0000,0000,,terms and a six from the second two terms. And whoa, look at that, our factored Dialogue: 0,0:00:46.85,0:00:52.19,Default,,0000,0000,0000,,form. So for any quadratic trinomial, we can try this process to factor it. We Dialogue: 0,0:00:52.19,0:00:57.28,Default,,0000,0000,0000,,can find two factors of a times c, that sum to the middle number b. We'll Dialogue: 0,0:00:57.28,0:01:02.03,Default,,0000,0000,0000,,rewrite the middle term using those factors and then try factoring by grouping.