That group factoring really makes it a lot easier, doesn't it? Definitely something for your notes.

Generally speaking, factoring a Quadratic trinomial is all about taking a polynomial, linked together by addition/subtraction and converting it to a multiplication problem. This is done by finding numbers that multiply to the first and last terms and add to the middle one. There are various algorithms you can use to accomplish this -- not just one. It's best to use an algorithm that use understand.

@JamesS-C You're weird.

Thanks

Juan well said

yup. It's like 1/3rd of his videos are talking about all his other videos...

I lost you in the exact same place.

You can solve by x² - 5x - 24 (x + 8)(x - 3) (3x + 4)(2x - 1) or 6x² - 8x + 3x - 4 2x(3x - 4) + 1(3x - 4) (2x + 1)(3x - 4) or x = 5 ± sqrt(25 + 96)/2 x = 5 ± 11/2 x = 8 x = -3 For factors change signs (x - 8)(x + 3) Divide by 6 and bring the denominator to front (3x - 4)(2x + 1)

The bit were you put the factors to the side is half the battle I think.

Okay, so basically he's smart and figured out that 6x^2 -5x -4 Is made up of several parts. 6x^2 = 3x(2x) That 3x is 3x(1)=3x That -4(2x)= -8x Then we've got like terms! 3x+ -8x = -5x; that's your b. And that -4(1)=4, your c. He factored it all at once. Factoring is the opposite of distribution.

the equation he found was 6x^2+3x-8x-4 so you spilt those equations up and you have 6x^2+3x… 3x(2x)= 6x^2 which is from the equation and 3x multiplied by 1 = 3x just like in the equation

Explained @ 15:33

I'll leave this here for posterity. Just had to multiply two negatives then add them to -8

You know how quadratic expression is ax^2 +bx +c? Well if your c is positive (the product) while your b is negative (the sum) it has to be two negative numbers. So the numbers are -3 and -5 and would be factored out as (x-3)(x-5).

@@ivetterodríguez-j4k Yeah. Honestly this is a terrible way of learning polynomial factorisation. Had to relearn the proper way haha.

I know something that's a little bit involving but once you get a hang of it, you can use it in all cases. Interested?

@@h_arks9691 What's the proper way? Sorry, I kinda like math and would not mind learning how to factor better.

Factoring By Grouping is the most common approach taught today, but there are others as well. I personally think that there are others, where the mathematical logic is easier to understand. Check out this video. The guy goes over 4 methods. kzfaq.info/get/bejne/a7epmL1osN2qe5s.html - I've seen even more than this.

Yes, it's called factoring.

From what mathematicians and scientists have told me, math is basically taught in such a way that, at least in the U.S., you learn processes first and the mathematical logic and applications later on. Personally, I think this is backwards -- because most people don't do well enough in math to ever make it to these higher-level math classes. Thanks to the internet, this is changing some, but many students at the lower levels are still being taught math by people who really don't understand it well enough to be teaching it. I equate this to someone having a degree in and being assigned to teach a language that aren't actually fluent in. From what I've noticed, engineers and other scientists make some of the best math teachers -- because they do math from a deeper understanding of concepts and mathematical logic. They also tend to think outside of the box, which is something I like.

Roger, unfortunately My whole life was wasted(half joking), now I'm catching up. Maybe help a Grandchild so (s)he might help others.

You're right. Analytical thinking is rarely seen, nowadays.

@@chocolateangel8743 It's also funny what having a bad math education can do to you. I basically missed out on 7th grade math, didn't take grade 8 math at all (pre-algebra), and took algebra 1 (grade nine math) for about 2 and half years. I won't go into details about how exactly this came to be in a youtube reply, but it did. After a few years of this stuff, I noticed my math skills begin to plummet. Now, it's like there's something blocking my mind from understanding, as you mentioned, mathematical logic and applications. I'm in 11th grade now, crawling through pre-calculus, and probably not going to pursue a grade 12 math credit unless it is absolutely necessary.

@@laurac.405 I get that. I'm sorry you had to go through that. I've actually heard math teachers and students talk about how kids "hit a wall" around 10th-grade math. It's very common. One thing I'd recommend is that you do some research on different learning styles, try some things, and see what works for you. It should be noted that you may not learn math the way you do other subjects. I know I don't.

Exactly