Back in 80s I was just trying get through high school, now my phone and youtube has help me get through college, and now I'm in my late 50s, with your help to pass my algebra class that I will be taking in 6 months prepared😊
I'm a mature student trying to cobble together some foundational knowledge and got myself waaaaay into the weeds with factoring polynomials. This was my breakthrough!!!!!!! Thank you so much!!
Greetings. Factoring the expression gives (2X+1)(3X-4). I usually concern myself with the middle term. In this case (2X)( -4) gives -8X, now we need to add +3X to get the result of -5X. Therefore (2X) should go in the first sets of brackets and -4 in the second sets of brackets. For our positive 3X we need to multiply 1 times 3X. These are our factors that must be placed in the different sets of brackets. Finally, we will group 2X +1 and 3X -4. Let us check, 2X times 3X =6X^2, 2X times minus 4= minus 8X, 3X times 1= positive 3X, minus 4 times positive 1 = Minus 4 and the result is 6X^ +(-8X +3X) -4 = 6X^2 -5X -4.
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.
cheers John. bought you course and love it. im 40 and going back to school. took the tsi and got a 957. I need a 960+ but I could tell just by doing the exam, the areas was weak in and in some cases didn't have clue. taking it again on Wednesday, fingers crossed
This helped me learn more! I am gonna dive into your videos more. I am terrible at math. It is literally like greek to me. I am in a college math and its online so its teach yourself in a way. I love this video. Thank you!!
I understood everything up until the 3x(2x+1)-4(2x+1), I don’t know where the (2x+1) came from, I understand what you were doing and how you got the other numbers but not the 2x+1. Any help, I’m taking notes on this and want to get it right, thank you.
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
So Im struggling with how to figure out which number to put first. Other tutorials have put the larger number of the factor/sum AbC chart first and it completely changes the answer
Cool! And yeah, a lot less brain-busting than what you showed at the end: starting with (ax ? b)(cx ? d) and just bootstrapping it. "Group factoring", yeah... bulletproof! If I was ever shown this in high school, I sure don't remember it at all. Oh, my teachers might have shown it, but it just didn't stick.
now that ive more of these its getting easier as a refresh (3x-4)(x+1) and correct..... so if you factor like this and is equals to 0 its x=4/3 and x= -1
Can somebody help me figure out "" x^2 -8x + 15 "". I can't figure how 3 + 5 ( the constant multiples; that actually only equal the reciprocal of 8) would work in brackets with x
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).
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. ruclips.net/video/5QyeZ7KwFKg/видео.html - I've seen even more than this.
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.
@@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.
Back in 80s I was just trying get through high school, now my phone and youtube has help me get through college, and now I'm in my late 50s, with your help to pass my algebra class that I will be taking in 6 months prepared😊
I'm a mature student trying to cobble together some foundational knowledge and got myself waaaaay into the weeds with factoring polynomials. This was my breakthrough!!!!!!! Thank you so much!!
There's nothing better during an exam, than to have a procedure that is "bulletproof". Thank you!
You put more effort advertising your other videos than effectively explaining how to factor trinomials.
Juan well said
yup. It's like 1/3rd of his videos are talking about all his other videos...
100 percent
Greetings. Factoring the expression gives (2X+1)(3X-4). I usually concern myself with the middle term. In this case (2X)( -4) gives -8X, now we need to add +3X to get the result of -5X. Therefore (2X) should go in the first sets of brackets and -4 in the second sets of brackets. For our positive 3X we need to multiply 1 times 3X. These are our factors that must be placed in the different sets of brackets. Finally, we will group 2X +1 and 3X -4. Let us check, 2X times 3X =6X^2, 2X times minus 4= minus 8X, 3X times 1= positive 3X, minus 4 times positive 1 = Minus 4 and the result is 6X^ +(-8X +3X) -4 = 6X^2 -5X -4.
I am a high schooler and have never been properly taught factoring of trinomials. Thank you!
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.
I have learned a new technique which I will also teach my students. Thank you so much.
cheers John. bought you course and love it. im 40 and going back to school. took the tsi and got a 957. I need a 960+ but I could tell just by doing the exam, the areas was weak in and in some cases didn't have clue. taking it again on Wednesday, fingers crossed
I'm 12 and a 7th-grade algebra student named Francisca, and I finally understand this!!!
That group factoring really makes it a lot easier, doesn't it? Definitely something for your notes.
I'm 40 and helping my daughter...after how many years, this finally makes sense!
This helped me learn more! I am gonna dive into your videos more. I am terrible at math. It is literally like greek to me. I am in a college math and its online so its teach yourself in a way. I love this video. Thank you!!
I understood everything up until the 3x(2x+1)-4(2x+1), I don’t know where the (2x+1) came from, I understand what you were doing and how you got the other numbers but not the 2x+1. Any help, I’m taking notes on this and want to get it right, thank you.
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
I was hoping you would have also shown the quadratic formula in this video.
@JamesS-C
You're weird.
Thanks
So Im struggling with how to figure out which number to put first. Other tutorials have put the larger number of the factor/sum AbC chart first and it completely changes the answer
15:38 how did you get 2x + 1 in the beginning?
Explained @ 15:33
tanks I just try to configurate how integrate the numbres
GOOD! Just found a new manner of doing this.
Cool! And yeah, a lot less brain-busting than what you showed at the end:
starting with (ax ? b)(cx ? d) and just bootstrapping it.
"Group factoring", yeah... bulletproof!
If I was ever shown this in high school, I sure don't remember it at all. Oh, my teachers might have shown it, but it just didn't stick.
you got me subscribed with this one chief
“put away your cell phone” sir i am watching this on my phone
Love you bro I’m like staying up doing this math work
now that ive more of these its getting easier as a refresh (3x-4)(x+1) and correct..... so if you factor like this and is equals to 0 its x=4/3 and x= -1
I will close shop for the day leaving while I'm ahead because I got this one right, thanks to the best factoring hack. :)
It would be great to get chapters in these videos.
Why sir we do factor of polinomial
This is better by naming the topic without saying “many will get this wrong.”
This vid helps reinforce Yesterday's. TYSM
Great vid wish I didnt give up on math years ago and found this instead; So I wouldnt dive into Calc and fail it easily 😬
Can somebody help me figure out "" x^2 -8x + 15 "". I can't figure how 3 + 5 ( the constant multiples; that actually only equal the reciprocal of 8) would work in brackets with x
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.
No idea were you got -3 2 and -2 3.
Wow. Nobody taught that method in the 70s.
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. ruclips.net/video/5QyeZ7KwFKg/видео.html - I've seen even more than this.
The answer is 3X −4 )2×+1)
Ans. (2x+1)(3x-4)
Your videos help me sm!
I love you bro
i am taking calculus in college and somehow have an A. i cannot factor to save my life. it is beginning to catch up to me..
YOU write down the answer then trying to explain it without working out where the answer came from, I don't get it.
This is reversed foiling.
Yes, it's called factoring.
🌹
He literally spent half the video doing nothing relevant at all.
Exactly
What percentage of the world ever uses this? .00001? I learned it because I had to. Complete waste of time.
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.
🙋🙋