@@MikehMike01 Well, you need to know the mathematical definition of what it means to factor (to write something as a multiplication problem) as well as what it means to factor a trinomial (the factors of the first and last terms should add up to the middle one). Beyond this, it's about trying out various algorithms and figuring out which one best suits you, based on your understanding of it. There are multiple algorithms (more than in this video), and even though I know a bunch of algorithms, even I have my preferences. Math is meant to be explored.
I think "Lazy AC" is a bad name, because "lazy" makes you feel bad for using it, but if it has been proven to work for all cases, why not use it? We dont have to prove, for example, that the area of a triangle is bh/2 everytime we use it, we just use it because it has been proven to work
I wasn't taught any of these methods. I was literally just told to find two expressions, resulting in me doing a lot of sloppy guesswork. Made things unnecessarily frustrating, especially when A was not equal to 1.
Yeah, that's literally how they also used to teach it in textbooks back then, but, as mentioned in my textbook, many people hated that method, so people came up the AC with Grouping method.
I always come back to this video when I forget how to factor trinomials and I swear that the slide and divide method is the only one that works for me!! Thank you once again 🥰
The Lazy AC method and 'slide and divide' are actually two variations of the same technique. The each rely on the zero product property insofar as either one or both factors of a quadratic expression are presumed to equal zero. Hence, if you can factor a non-zero number out of a binomial that is presumably zero whatever remains is then still equal to zero. I used to like 'slide and divide' best; esp. after the first time I saw this video. In the meantime I discovered Po Shen Lo's method of solving quadratic equations. I now prefer Po Shen Lo's method to factoring, CTS, or the quadratic formula.
You are my HERO! I have cried and cried trying to figure this out and I don't know what I would have done without this help. You may have saved me from dropping out. THANK YOU!!!
I enjoyed the Tic-tac-toe method. As someone who can factor in their brain quickly it takes out a lot of the writing steps and leads to an easy to interpret final result (but any teacher can see how you got it)
U are amazing man u helped me for my exam amazing........ I was preparing for my exam from other RUclips channel but I did not understand but u explained me ...... So thank you for that
This guy totally ROCKS! I'm trying to help my 8th grade son and I haven't dealt with this math in 40 years! This guy made it happen! Wish I had him in high school! LoL
THANK YOU!!! I have learned the 4th method in high school, I have always used it and it's AMAZING. I thought it was known. Anyways, years passed and I kind of forgot how to do it, and I got shocked when I tried to look it up because I couldn't find it anywhere. Everyone explains the other methods, no one knowns about the tic tac toe method... (my teacher used to call it a different name). I was really devastated because I wanted to remember it but I couldn't find anyone who knows about it, until I finally found your video!! Thank you!! I recalled it immediately I just needed this trigger, you're awesome. The tic tac toe method has always been the best.
Mine is similar to the 2nd method. However I used fractions. So we have the 2 factors of -24 which is -8 and 3 that adds up to -5. Now we divide the factors by a which is 4. So now we have -8/4 and 3/4. Now we simplify both fractions if possible. If the fraction becomes a whole number, put a 1 in the denominator. So now we have -2/1 and 3/4. The denominators are for the coefficients that are linked to the variable x and the numerator becomes the constant. So we will have (1x-2)(4x+3) or (x-2)(4x+3)
At first I thought I'd like the lazy AC method, however when you get into more complex trinomials with bigger numbers (ex. 21xˆ2 + 43x + 20), it get's too crazy. TIC TAC TOE METHOD!!!!!!! I just tried it with 2 examples. Eaaazzzzybreeezy. Thank you!!! You are so enthusiastic and beyond hilarious.
I really liked the Lazy AC. Very well explained. I will definitely be searching for more of your videos. I was really lost but just this video explained it all. Thank you.
i know this is really old but normally i'd use the splitting the middle term one which is a variation of your first technique however, the lazy ac method is so fast and ive never heard of it before, thank you for introducing this to me
The AC Method + Grouping and "Splitting the Middle Term" are the same thing. As for the "Lazy AC Method," it's actually a shortcut for the Australian method for factoring trinomials. It works by compensation. If you look up "the bottoms-up method for factoring trinomials," you will see it's basically the same thing. All of these similar approaches are based on the same principle. They are just presented slightly differently.
Hate to be a stickler for terminology, but these are quadratics(ax^2+bx+c where a,b, and c are constants). A trinomial has either three variable terms such as (x+y+z) or two variable terms and a constant term such as (x+y+1). I point this out because similarly to the binomial theorem and binomial distribution there exists a trinomial theorem and trinomial distribution as well as a more general multinomial theorem and multinomial distribution
Great, because I did not understand the slide and divide method that our daughter is being taught. After seeing the AC method, I understand the magic. I think I like AC method because you can check each step ("is it equal? yes or no."). the other methods involve memorization without understanding, so I don't like them as much. Maybe o.k. for better students than me who can keep in mind the theory behind the other methods, but for me I need to see something where every step makes sense. Thanks Blackpenredpen for being so clear.
My preferred method is completing the square/the quadratic formula, because they work just as well in any field without having to do guesswork/brute-force for factoring numbers. All I need to know is how to find square roots(if they exist) in the given field (And of course how to find multiplicative inverses, and addition and multiplication in the given field, but that's part of a field's definition so that's ez)
Hello rpbp, I would like to know if the lazy ac method and the slide and divide method works if a is negative. I love your videos and your way of teaching. That has helped me a lot btw.
In principle, it should. In practice, if I need to factor a trinomial where a is negative, I find it easier to factor out the negative and go from there: -2x^2 + 5x - 2 becomes -(2x^2 - 5x + 2). If the factoring is for the purpose of solving a quadratic equation, it's even better: If -3x^2 + 8x - 2 = 0, then 3x^2 - 8x + 2 = 0 as well.
Dear Sir, I like your math so much. I remember you once explained the cross method in different regions such as Taiwan, Hong Kong, and the United States in Chinese. However, I can't find this video now. Could you please tell me where I can find this video? Thank you!
My system that I have always used is similar to the last one, but I do not set it up as tic tac toe. I list all the factors of 4 on the left side and all the factors of 6 on the right side and see which combination gives me the answer. edit: I like it because I do not like steps that I have to remember. I like to understand what I am doing. The last one without setting up as a tic tac toe does that for me.
I vaguely remember seeing the diagram, and of course the quad formular, but only use it for non trivial factors. I guess I use the 4th method, but in my head rather than formally. Yes, there is a choice of +/- 1 x -/+ 6 or +/- 2 x -/+ 3, but which one x4 plus the other results in 5? Can only be 4x2 and 3. Then determine the signs to get -5.
I think I like the first method the best today, ac plus grouping. It reminds me of partial fraction decomposition. Both make me think about grouping in a way I didn't earlier, which is good brain development. Thanks for the tips.
If a=1, I normally try to find two numbers adding to b and multiplying to c, just as in the first three methods. The two numbers will then go inside the parentheses. Otherwise, doing the quadratic formula in my head is quicker for me than any of these methods (and requires no guessing). I might guess as in the fourth method if both a and c are prime, though, since that reduces the number of options (of course assuming rational roots).
3rd method is the fastest one. It can be improved and you can directly write the answer. Solve m*n=ac and m+n=b for m and n. The answer is (x+m/a) (x+n/a) =0
Thank you, I am here just for a quick review, and as always your videos are funny and interesting, I think I could watch your math videos all day long.
I think that all the methods are actually the same thing behind the curtains, but organized in different ways. This techniques are hard to apply to trinomials with arbitrary coefficients, but for the integer coefficients case it should come in handy... if you are not willing to factor the expression by first finding the polynomial roots. Here's yet another 'guessing' strategy that works for this cases and sometimes higher grade expressions: given a polynomial expression with integer coefficients, use the Rational Root Theorem to find all possible rational candidates r that could appear in an (x-r) factor. Then try polynomial division of your expression with (x-r), for each candidate (this division can be done quite fast using Ruffini's rule). If/when the remainder of the division is zero, you've factored a linear term!!!
Hi I m nasrin .I like your different math technique. Thankyou so much sir.now I practice pert test math.because i m going to admit college.so i prepare my self for pert exam.i m oversis student. Sometimes I want your help sir .pl help me for pert exam.
loved the video. I have always been using the lazy method its the best and fastest for tests. taught it to my friends and told them about your video as well
I'm honestly surprised that this, being the first video that I clicked, was able to teach me how to factor better than my teacher. Thank you so much.
I am glad to hear!!!
@@blackpenredpen hoping it works for me too bc i am BEHIND rn
this video has the benefit of you already knowing everything your teacher taught you
@@MikehMike01 Well, you need to know the mathematical definition of what it means to factor (to write something as a multiplication problem) as well as what it means to factor a trinomial (the factors of the first and last terms should add up to the middle one).
Beyond this, it's about trying out various algorithms and figuring out which one best suits you, based on your understanding of it. There are multiple algorithms (more than in this video), and even though I know a bunch of algorithms, even I have my preferences. Math is meant to be explored.
@@chocolateangel8743 bruh too many words
You're a life saver dude. Thank you so much for this video! If I had you as a teacher I wouldn't mind math.
11:11 "it's a fraction, that's no good"
oh man if I had a nickel for every time I had that thought on a test
Now what happens when you start having fractions of a nickel?
a nickel is a fraction of a dollar, so you my friend, just fricked yourself
slide and divide is the most horrible technique i've ever seen. doesn't follow math rules like lazy ac. but somehow it's even more work???
@@Tsunami0950I have a penny, 1/5th of a nickel.
Excellent job. And of course the Lazy AC is my choice.
Rod Galloway thank you!
Thank you for this fantastic video !
The lazy AC is the fastest and the most practical in my opinion.
thanks
Welcome
URon M ,
Ron M but you have to make sure that the trinomial can be factored
I think "Lazy AC" is a bad name, because "lazy" makes you feel bad for using it, but if it has been proven to work for all cases, why not use it? We dont have to prove, for example, that the area of a triangle is bh/2 everytime we use it, we just use it because it has been proven to work
I wasn't taught any of these methods. I was literally just told to find two expressions, resulting in me doing a lot of sloppy guesswork. Made things unnecessarily frustrating, especially when A was not equal to 1.
frozenbacon same here all I was taught to do is to basically do trial and error so I was just stabbing in the dark untill I got the answer
Yeah, that's literally how they also used to teach it in textbooks back then, but, as mentioned in my textbook, many people hated that method, so people came up the AC with Grouping method.
Exactly
@MsWilson
@@shaunakkulkarni4679 I can agree to that as long as the coefficient, a, equals 1.
I always come back to this video when I forget how to factor trinomials and I swear that the slide and divide method is the only one that works for me!! Thank you once again 🥰
What if the quadratic is normalized (i.e. a = 1) already?
Thank you. And for your questions
I solved
(X+4)(5x-2).
Overrated comment
The Lazy AC method and 'slide and divide' are actually two variations of the same technique. The each rely on the zero product property insofar as either one or both factors of a quadratic expression are presumed to equal zero. Hence, if you can factor a non-zero number out of a binomial that is presumably zero whatever remains is then still equal to zero.
I used to like 'slide and divide' best; esp. after the first time I saw this video. In the meantime I discovered Po Shen Lo's method of solving quadratic equations. I now prefer Po Shen Lo's method to factoring, CTS, or the quadratic formula.
Thanks!
Nothing more satisfying than the matching pair in the grouping method.
Three weeks of classes couldn’t teach me what he did in 5 minutes.
Ailith S it really is a shame
You are my HERO! I have cried and cried trying to figure this out and I don't know what I would have done without this help. You may have saved me from dropping out. THANK YOU!!!
I enjoyed the Tic-tac-toe method. As someone who can factor in their brain quickly it takes out a lot of the writing steps and leads to an easy to interpret final result (but any teacher can see how you got it)
I finnally found the BEST method in the world man the tic tac toe is so nice it works always and it is so easy to see your mistakes.
Tanks man!
8Med9Zonder I am very glad to hear it! : )
Yessss man the tic tac toe one
works if your fast at math
U are amazing man u helped me for my exam amazing........ I was preparing for my exam from other RUclips channel but I did not understand but u explained me ...... So thank you for that
As a teacher I just teach complete the square and quadratic formula. All this guess and check is mind numbing.
This guy totally ROCKS! I'm trying to help my 8th grade son and I haven't dealt with this math in 40 years! This guy made it happen! Wish I had him in high school! LoL
Thanks so much! I liked the slide and divide one the best. The last one just seems pretty complicated with how they have to match up.
You're welcome! Thanks for watching as well = )
THANK YOU!!! I have learned the 4th method in high school, I have always used it and it's AMAZING. I thought it was known. Anyways, years passed and I kind of forgot how to do it, and I got shocked when I tried to look it up because I couldn't find it anywhere. Everyone explains the other methods, no one knowns about the tic tac toe method... (my teacher used to call it a different name). I was really devastated because I wanted to remember it but I couldn't find anyone who knows about it, until I finally found your video!! Thank you!! I recalled it immediately I just needed this trigger, you're awesome. The tic tac toe method has always been the best.
I am very happy to receive your comment Sara! Thank you as well!
The first method was the best😀
Mine is similar to the 2nd method. However I used fractions. So we have the 2 factors of -24 which is -8 and 3 that adds up to -5. Now we divide the factors by a which is 4. So now we have -8/4 and 3/4. Now we simplify both fractions if possible. If the fraction becomes a whole number, put a 1 in the denominator. So now we have -2/1 and 3/4. The denominators are for the coefficients that are linked to the variable x and the numerator becomes the constant. So we will have (1x-2)(4x+3) or (x-2)(4x+3)
I am a newly hired professor. I teach remedial math. I will definitely show these methods to my students. Thank you. 😊😊😊
I love you.
How come a half a week of my teacher teaching this isn't as good as watching 6 minutes of this.
Thanks a lot , you helped me more in 6 minutes than 2 teachers in the periods ( 2 hours)
In less than a minute you explained what I've been struggling with for days. why does something so easy have to be so difficult?
At first I thought I'd like the lazy AC method, however when you get into more complex trinomials with bigger numbers (ex. 21xˆ2 + 43x + 20), it get's too crazy. TIC TAC TOE METHOD!!!!!!! I just tried it with 2 examples. Eaaazzzzybreeezy. Thank you!!! You are so enthusiastic and beyond hilarious.
Your a good teacher you inspired me
I really liked the Lazy AC. Very well explained. I will definitely be searching for more of your videos. I was really lost but just this video explained it all. Thank you.
The lazy AC Method really helped me a lot.
I totally understood this. I am doing online college and this was the best learning video I have seen. Very easy to understand. Thank you so much.
Thank you so much!!!!!!
Best factoring video I've come across, thank you!
Tic Tac Toe method was awesome! You friggin ROCK!!! Thank you so much!
WTF
I can do it right now
Thanks man;)
Thank you so much. 😁 Slide and divide for me
All I have to say is...you're a life saver and a wonderful teacher!
i know this is really old but normally i'd use the splitting the middle term one which is a variation of your first technique however, the lazy ac method is so fast and ive never heard of it before, thank you for introducing this to me
The AC Method + Grouping and "Splitting the Middle Term" are the same thing. As for the "Lazy AC Method," it's actually a shortcut for the Australian method for factoring trinomials. It works by compensation. If you look up "the bottoms-up method for factoring trinomials," you will see it's basically the same thing. All of these similar approaches are based on the same principle. They are just presented slightly differently.
Hate to be a stickler for terminology, but these are quadratics(ax^2+bx+c where a,b, and c are constants). A trinomial has either three variable terms such as (x+y+z) or two variable terms and a constant term such as (x+y+1). I point this out because similarly to the binomial theorem and binomial distribution there exists a trinomial theorem and trinomial distribution as well as a more general multinomial theorem and multinomial distribution
Like them all. Makes it not so boring having variety of options. Grid method though is my favorite. Makes you feel like your about to play a game.
Great, because I did not understand the slide and divide method that our daughter is being taught. After seeing the AC method, I understand the magic. I think I like AC method because you can check each step ("is it equal? yes or no."). the other methods involve memorization without understanding, so I don't like them as much. Maybe o.k. for better students than me who can keep in mind the theory behind the other methods, but for me I need to see something where every step makes sense. Thanks Blackpenredpen for being so clear.
I am very happy to help!! Thank you Alicia for your nice comment.
Lazy AC is my favorite but all these methods were easy to understand
My preferred method is completing the square/the quadratic formula, because they work just as well in any field without having to do guesswork/brute-force for factoring numbers. All I need to know is how to find square roots(if they exist) in the given field (And of course how to find multiplicative inverses, and addition and multiplication in the given field, but that's part of a field's definition so that's ez)
THANKS FOR THE VIDEO.ALL THE METHODS ARE GREAT, BUT I LOVE THE LAZY AC
the grapefruit technique helped me the most
I use the quadratic formula :
》 x = -b ± √b²-4ac/2a
: )
Thank you . Way much easier to understand .
I LOVE the slide and divide
Bro I literally love u dude thanx for makiiiing this video😭😭😭😭
Hello rpbp, I would like to know if the lazy ac method and the slide and divide method works if a is negative.
I love your videos and your way of teaching. That has helped me a lot btw.
In principle, it should. In practice, if I need to factor a trinomial where a is negative, I find it easier to factor out the negative and go from there: -2x^2 + 5x - 2 becomes -(2x^2 - 5x + 2). If the factoring is for the purpose of solving a quadratic equation, it's even better: If -3x^2 + 8x - 2 = 0, then 3x^2 - 8x + 2 = 0 as well.
This was a LIFESAVER ,thank you!
Dear Sir, I like your math so much. I remember you once explained the cross method in different regions such as Taiwan, Hong Kong, and the United States in Chinese. However, I can't find this video now. Could you please tell me where I can find this video? Thank you!
My system that I have always used is similar to the last one, but I do not set it up as tic tac toe. I list all the factors of 4 on the left side and all the factors of 6 on the right side and see which combination gives me the answer.
edit: I like it because I do not like steps that I have to remember. I like to understand what I am doing. The last one without setting up as a tic tac toe does that for me.
I recently saw that -- and like it a lot. Once you get used to it, it's really quick. I think it can take more practice than other methods, tough.
The tic-tac-toe method helped a lot! Thank you v much!:)
Glad to hear!!!
For me it that would take too long for a test...
Than you so much for the video man, now I can practice this with my kids. Slide and divide is so easy.
I vaguely remember seeing the diagram, and of course the quad formular, but only use it for non trivial factors.
I guess I use the 4th method, but in my head rather than formally.
Yes, there is a choice of +/- 1 x -/+ 6 or +/- 2 x -/+ 3, but which one x4 plus the other results in 5? Can only be 4x2 and 3. Then determine the signs to get -5.
Lazy AC is the bomb! Thanks man! Your the best!
I love this man with all my heart. He's so wholesome!
I am all about that "slide and divide!"
Hello!
AC grouping worked best for me. Thank you sire.
Thank you so much you really helped !!! I have a quiz tomorrow and I feel a lot more confident
I think I like the first method the best today, ac plus grouping. It reminds me of partial fraction decomposition. Both make me think about grouping in a way I didn't earlier, which is good brain development. Thanks for the tips.
If a=1, I normally try to find two numbers adding to b and multiplying to c, just as in the first three methods. The two numbers will then go inside the parentheses. Otherwise, doing the quadratic formula in my head is quicker for me than any of these methods (and requires no guessing). I might guess as in the fourth method if both a and c are prime, though, since that reduces the number of options (of course assuming rational roots).
I can't decide whether to use lazy ac or slide and divide, but they are both so much easier than the method I used to use
They are basically the same thing.
I love the slide and divide method
I liked the slide and divide method the best!
I knew the first one and the last one technique but the others only now. Thanks for sharing man.
3rd method is the fastest one.
It can be improved and you can directly write the answer.
Solve m*n=ac and m+n=b
for m and n.
The answer is
(x+m/a) (x+n/a) =0
Thank you so much!!!! This video helped me a lot and I aced my test:)
Thank you, I am here just for a quick review, and as always your videos are funny and interesting, I think I could watch your math videos all day long.
exellent :) thanks a lot other videos only showed slide method which confused me :( but this made me get it so much appreciated
Lazy AC Method for me.Thanks & more power to your show❣️
I would love to see BPRP try drawing dotted lines on a blackboard
Wow i was struggling with trinomials and now i understand
AC method plus grouping is my favorite.
Thanks by thr the way this video helped
Love slide and divide, I don't have to do any guesswork!
Really good should have u as my math tutor
I use last one because i practices for a long time, I use denominator and trial in my brain.
I think that all the methods are actually the same thing behind the curtains, but organized in different ways. This techniques are hard to apply to trinomials with arbitrary coefficients, but for the integer coefficients case it should come in handy... if you are not willing to factor the expression by first finding the polynomial roots.
Here's yet another 'guessing' strategy that works for this cases and sometimes higher grade expressions: given a polynomial expression with integer coefficients, use the Rational Root Theorem to find all possible rational candidates r that could appear in an (x-r) factor. Then try polynomial division of your expression with (x-r), for each candidate (this division can be done quite fast using Ruffini's rule). If/when the remainder of the division is zero, you've factored a linear term!!!
I love the slide and divide method :)
5:47
You are the best at explaining that!!!!!!
Tic tac toe factoring is the best. Imma just use that from now on lol
Thank you! You explained this with great clarity!
you just save my life lololll very useful first technique is my favorite
I prefer the slide and divide method - easier to do in your head, I think.
AC + grouping is still my favorite, but thanks for showing some options :)
AC + grouping is the method I learned at school, but I prefer slide and divide.
Hi I m nasrin .I like your different math technique. Thankyou so much sir.now I practice pert test math.because i m going to admit college.so i prepare my self for pert exam.i m oversis student. Sometimes I want your help sir .pl help me for pert exam.
Thanks, man you helped me with my homework and test!!!!
God bless this man ❤️
I'm trying to apply the first method to 3x^2-11x-4, but after Foil-ing the final factors, it gets the wrong answer. Why is this?
@@muadhnate thank you! This was very helpful, I messed up after getting the mutiples of 1 and 12.
@@muadhnate so, I have a question. You go from 3x^2-12x+1x-4 to 3x(x-4)+1(x-4). Where did you get that -4 from in 3x(x-4) ?
Thanks this was sooooo super helpful.
First three only work sometimes but I love method 4. Thnx so much u da GOAT
If you are not working as a teacher i strongly recommend you start :D amazing video :O
loved the video. I have always been using the lazy method its the best and fastest for tests. taught it to my friends and told them about your video as well
sabin ghimirey thank you!
I LOVE YOU SO MUCH YOU ARE BETTER THAN MY SCHOOL TEACHER THANK YOU
wow amazing..thank you sir...i will apply this to my students..
The final method is the best.
thank you for the video, but I couldn't do a trinomial with the AC method.
5x²+2x+10
How would you solve this quadratic equation 2x^2 -13x+42