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.

@blackpenredpen

6 жыл бұрын

I am glad to hear!!!

@mojodojo5112

3 жыл бұрын

@@blackpenredpen hoping it works for me too bc i am BEHIND rn

@MikehMike01

2 жыл бұрын

this video has the benefit of you already knowing everything your teacher taught you

@chocolateangel8743

2 жыл бұрын

@@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.

@MikehMike01

2 жыл бұрын

@@chocolateangel8743 bruh too many words

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

@Tsunami0950

Жыл бұрын

Now what happens when you start having fractions of a nickel?

@theburger_king

Жыл бұрын

a nickel is a fraction of a dollar, so you my friend, just fricked yourself

@garylangford6755

3 ай бұрын

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???

@CalculusIsFun1

9 күн бұрын

@@Tsunami0950I have a penny, 1/5th of a nickel.

Finally found the first mathematician with swag

@blackpenredpen

7 жыл бұрын

THANKSSSS!

@swizzi4794

6 жыл бұрын

Helped, thank you

@s4mwize

5 жыл бұрын

Check out Cédric Villani, he got plenty of it :d

@epicgaming7871

4 жыл бұрын

LMAO

@ramakrishnasen4386

3 жыл бұрын

Wtf even!? You clearly haven't seen enough mathematicians maybe

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.

Best math teacher ever!!! He does an outstanding job. He explains it so well. Calmly and simply. Many methods to choose from. Thorough and detailed. With a dash of humor.

Excellent job. And of course the Lazy AC is my choice.

@blackpenredpen

7 жыл бұрын

Rod Galloway thank you!

I like AC lazy the most.

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 🥰

@wyattstevens8574

Жыл бұрын

What if the quadratic is normalized (i.e. a = 1) already?

Thank you for this fantastic video ! The lazy AC is the fastest and the most practical in my opinion.

@blackpenredpen

7 жыл бұрын

thanks

@Ronnie7X

7 жыл бұрын

Welcome

@mariagalvarro5463

7 жыл бұрын

URon M ,

@zorm_

7 жыл бұрын

Ron M but you have to make sure that the trinomial can be factored

@dcs_0

7 жыл бұрын

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

username: blackpenredpen in the video: *uses chalk* Username: Am I a joke to you?

@calibr0636

4 жыл бұрын

r/usernamedoesntcheckout yes i know there is no such subreddit, but there is one called r/usernamechecksout

@shosad5934

3 жыл бұрын

I mean, he does use a red and white chalk so it does kind of work

@SMartin-bg2jy

3 жыл бұрын

whitechalkredchalk

@Fat380

3 жыл бұрын

funny...

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.

@isaacreed1241

6 жыл бұрын

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

@MusicalInquisit

6 жыл бұрын

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.

@SpringRain23

5 жыл бұрын

Exactly

@Tanaglias

5 жыл бұрын

@MsWilson

@MusicalInquisit

5 жыл бұрын

@@shaunakkulkarni4679 I can agree to that as long as the coefficient, a, equals 1.

Thank you so much. This probably the best teaching video I have ever viewed. It is completely on-topic, describes everything in full detail, and now I can actually understand factoring binomials. You just saved a student from failing a quiz.

I wasn’t able to understand this in class no matter how much I focused, but your way of teaching helped me learn how to factor trinomials in just 5 minutes!! Thanks for this! just subscribed

turn caption on and read 7:52

@veylaemelee3951

6 жыл бұрын

thx i needed that

@adamglenn6826

6 жыл бұрын

I'm down

@swizzi4794

6 жыл бұрын

OH.MY.GOSH

@hungryfareasternslav1823

5 жыл бұрын

You won a Nobel Prize!

@DlcEnergy

5 жыл бұрын

7:54 lets look at porn ey? can we reduce that? 6:35 *_draws boobs_*

Slide and divide is my favorite. It's just so much simpler for me. Thank you!!

I ended up sticking with the AC method, but I just want to say that the way you teach, with kindness, made me smile through the video. Thank you for being who you are and for helping us out!

Three weeks of classes couldn’t teach me what he did in 5 minutes.

@-kat

4 жыл бұрын

Ailith S it really is a shame

This was much more helpful than my teacher's explanation. Thank you so much for your help!

Slide and Divide is for sure my personal favorite, thank you!

I love how this is the only tutorial on how to do something in math and is understandable

Thank you. And for your questions I solved (X+4)(5x-2).

@alphazero339

Ай бұрын

Overrated comment

I like the slide and divide :) Thank you :)

I'm 32 and going back to college. Your 4th and final method resonated most with me. Being able to check the math right there worked wonders. The amount of potential solutions threw me for a loop and caused me much frustration- but your video has helped me solve this riddle. Thank you for the guidance and advice.

Thank you , Mr.blackpenredpen my favourate slide and divide

OMG this was a huge help thanks so much!!!!!!!!!! I love the tic tac toe one it's really helpful and anyone could easily understand it. I was literally crying looking for videos to understand this concept and you made that happen, thank you so much!

@blackpenredpen

7 жыл бұрын

Roziya Alla Noor I am very to hear. Best of luck in your class. : )

@rosaallanoor8530

7 жыл бұрын

Thank you!

That is great. Cannot wait to teach this to my middle school students.

@StoopVital

7 жыл бұрын

you have to look up videos on something you were hired to already know?

@blackpenredpen

7 жыл бұрын

I do the same too! I watch other people teaching to get new ideas. KZread is amazing that allows me to learn from other teachers. Thank you both for watching my video.

@navjotsohal1598

6 жыл бұрын

StoopVital LMAO

@btdpro752

6 жыл бұрын

StoopVital They look up videos because maybe they aren't good at explaining it according to previous students.

@ti84satact12

5 жыл бұрын

@@StoopVital No teacher knows everything AND we should be able to honestly admit that. Maybe she just wanted to give her students more OPTIONS to choose from. A great quality in a teacher in my opinion.

Thanks a lot , you helped me more in 6 minutes than 2 teachers in the periods ( 2 hours)

Lazy AC is my go-to from now on. Thank you so much for this video!!!

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.

@Someone-np4iq

Жыл бұрын

Thanks!

I'm honestly surprised that he taught this so much easier, simpler, and quickly, than my teacher could have.

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!!!

awesome....been struggling with factoring and this was very helpful...thank you!

The first method was the best😀

My prefered method is 5: quadratic formula.

@ZipplyZane

6 жыл бұрын

The quadratic formula is not at all useless. Though using it to factor requires ingenuity. You get the answers for y = 0, but then have to figure out the coefficients. This can be quicker, but usually isn't.

@trueriver1950

6 жыл бұрын

ZipplyZane speak for. yourself. The square root is always of a perfect square if the trinomial is factorisable so its very fast to calculate the roots. You just subtract the roots from x within each factor. Then multiply by denominators to get integer values in the factors Speaking for myself i can always do this faster than any of the methods shown. Of course different folk have different skills and you have discovered that another technique works better for you. Thats cool too - just please do remember that it wont be the case for everyone...

@AlgyCuber

6 жыл бұрын

me too

@Koisheep

6 жыл бұрын

I've never ever studied the methods in the video. Method number 1 was mentioned in my high school books but I applied it only once and already in college. Even when we had a subject all about factoring polynomials in college, we used the good ol' quadratic formula

@snbeast9545

5 жыл бұрын

I'd prefer lazy ac to having to do a lengthy formula.

Best factoring video I've come across, thank you!

After wasting my time with several videos I found the one I was looking for. Thank you so much, keep up the good work. I finally got the concept of factoring.

Thank you so much!!!!!!

As a teacher I just teach complete the square and quadratic formula. All this guess and check is mind numbing.

I think my favorite method is the AC method and I've been using it since I watched this video. Thanks so much!

Tic Tac Toe method was awesome! You friggin ROCK!!! Thank you so much!

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!

@blackpenredpen

6 жыл бұрын

8Med9Zonder I am very glad to hear it! : )

@yafettegbaru3887

5 жыл бұрын

Yessss man the tic tac toe one works if your fast at math

My prefered method is the regular AC

I love this man with all my heart. He's so wholesome!

Thank you! You explained this with great clarity!

The best in my opinion is the standard "factoring by grouping". Simple, safe, and won't cause confusion later on (in case you forgot how to do the other methods). However, the other methods are also nice, and your videos are very educating and entertaining for math geeks like me. By the way, have you checked the email I've sent to you earlier regarding the integral of sqrt( 1 + 81 X^4 ) dx? Wolfram Alpha shows me the integration result, but it's kinda odd, and includes elliptic integrals and that sort of things which I don't understand.

@idk54756

7 ай бұрын

grouping only works when degree > 2

I was taught a different one: solve for X and then the polinomial is equal to a · (x-answer one) · (x-answer two)

@SimsHacks

3 жыл бұрын

Yeah but this works in every case.. you factor out in order to solve for roots really fast, solving for root to factor is pretty meh

@ttsookoo

3 жыл бұрын

Demonstrate an example please. Lol😅

@carviryzen288

3 жыл бұрын

@@ttsookoo lets say you have the polinomial 2x^2 -10x + 12, so a=2, b=-10 and c = 12. First, you set it equal to 0, then you solve for x and you get that the answers are 2 and 3. And in the end, 2x^2 -10x +12 = 2 (x-3) (x-2). In general, ax^2 + bx + x = a (x - 1st root of the polinomial) (x - 2nd root of the polynomial)

@chicchi1682

3 жыл бұрын

What do you do when the leading coefficient is one and can't be factored out?

@carviryzen288

3 жыл бұрын

@@chicchi1682 then a=1, so you still get p(x) = 1 • (x - 1st solution) • (x - 2nd solution)

honestly really loving this channel

Thank you so much for the help! The Slide method works very well and helped me to understand factoring trinomials!

Am I the only person thinking that he looks like he’s holding an ood translation sphere?

@myshasaeed5116

4 жыл бұрын

Bruh it's called a snowball mic

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.

@blackpenredpen

7 жыл бұрын

You're welcome! Thanks for watching as well = )

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.

You saved my life!!! Online school and algebra factoring drills don’t go together 😭😭

I just did it by utilizing the 3B1B easy quadratic formula, which works even when its not factorable with rational or real numbers, and there's no guess and check required, you should check it out

@blackpenredpen

4 жыл бұрын

I was there yesterday

You saved my ass, thank you so much! The AC method helps me a lot!

The slide and divide is my favorite, thank you so much

TIC-TAC-TOE method just helped me immensely!!! Thank you :)

WTF I can do it right now Thanks man;)

There is a rigorous variant of the lazy A.C... Write T = the trinomial. Then on the next line multiply T by A so in your example you would get 4 T = ( 4 x + ___ ) ( 4 x + ___ ) This works because you multiplied x by A twice, but only need to do so once. Then proceed as in the video and you will find the extra A will factor out in one of two ways. It might factor out of one term as in your example, or you may find that both terms factor and the two factors together multiply to A. I prefer this method as it is easy to do and ALSO easy to understand why it works. But stepping back from my favourite, as a teaching technique I very much like your approach of giving students choices in how to do this--I think in a typical class you will have different people liking each method. It is good teaching and ALSO letting them discover their own sense of mathematical style

I have only recently discovered your channel. I am a returning college student after taking a few years off. It has been 4 years since I have taken any kind of mathematics course and this video has been a life saver to me! I am struggling to understand the basics of earlier math courses and it has impeded my studies. Khan academy videos and SPECIFICALLY this video have really helped me. Thank you :)

I knew about the 1st and 3rd, thanks for the other two methods. Keep up the great work!!

For me it's easier finding the roots with the quadratic formula and then: a(x - root1)(x - root2) Good video

@johnnolen8338

6 жыл бұрын

Alexis Caraballo That's exactly what you're doing when you use the "slide & divide" method. The quadratic formula always works, but you shouldn't need to use it when the original expression can be factored. That's kind of the point. Using the quadratic formula on a factorable polynomial is like using a jackhammer to crack a walnut. It's overkill.

@gustavoantonio194

6 жыл бұрын

Alexis Caraballo same but then I realized it’s not practical to work efficiently, so now I’m here

@03_trivenibane67

6 жыл бұрын

Grt

@khbye2411

6 жыл бұрын

This formula mtd is guaranteed to work. so under stressful conditions (in eg timed exams) when your brain just stops working, it might be more useful to rely on the quadratic formula mtd than guess n check. And I guess this mtd would be super useful when dealing with quadratic equations with complex roots

@khbye2411

6 жыл бұрын

But if can use calculators in exams to solve for the roots of a quadratic eqn, then this would be the fastest and most reliable mtd

(5x-2)(x+4)

@salamander9763

7 жыл бұрын

Is that the answer of the 4x^2+ 18x+15?

@chadisaklaway7898

7 жыл бұрын

Salamander It is the answer to the problem at 16:30.

Thank you, so so much! Your videos are so appreciated! (My favorite is the Tic-Tac-Toe method).

All I have to say is...you're a life saver and a wonderful teacher!

for the ac method how come sometimes you still need to break it apart but sometimes thats the answer?

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?

This was a LIFESAVER ,thank you!

Thank you! I will need more practice to see my preference, but it will definitely be on my rewatch list!!!

Better to understand why and how factoring works than to memorize a method or trick to get the right answer. The point of factoring is to determine what two numbers are multiplied together when all you are given is the finished product of multiplication. The reason we factor polynomials is that polynomials represent a number, but with variables inside the number itself. The question becomes, how do we multiply numbers when we don't know what the variables inside a number are? The answer is that we distribute, so that even if the variable takes on any value, it does not change the result of multiplying by the number we distribute. Factoring asks the question: "what did we distribute by?" The answer is the GCF of the finished product of multiplication. When we factor, we are dividing our number by our GCF in order to reverse the process of multiplication. Then we write any number, including polynomials, in factored form by writing GCF * remaining values. The annoying part of this is that you have to know your multiplication facts well enough to be able to see what multiplied what in your head. This is what we do when we split a trinomial into a 4 term polynomial so that we can factor it with grouping. And by the way, factoring with grouping is precisely splitting up a polynomial with no uniform GCF into two groups that each have their own GCF's, then we factor each separate group in order to make an expression with does have one GCF for all terms, then we finish by factoring this last term to get the final factored product. This is exactly how and why factoring works. Now these tricks in this video can help make it easier for you to choose the correct two middle terms, but it doesn't make sense to learn the tricks before you understand what I just wrote above.

@MichaelRothwell1

5 жыл бұрын

Robert Wilson III If I understand you correctly, what you are saying is something like this: If you start with a quadratic factorised into two linear terms, and then multiply out using distribution, we initially get 4 terms. Then when we combine the two terms in x to get a single x term and end up with a standard three term quadratic, we "hide" the original distribution process. So when we want to factorise we have to separate the x term back into two x terms to "reveal" how the distribution was done and so reconstruct the original factorisation.

I want the lazy ac because I am lazy.

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.

@blackpenredpen

6 жыл бұрын

I am very happy to receive your comment Sara! Thank you as well!

OMG! The best method I've seen so far when factorizing quadratic equation! Very well-explained indeed... Lazy AC is my best choice. Thanks much brother...

@chocolateangel8743

2 жыл бұрын

It's actually the Australian method for factoring trinomials.

My Person choice would be the tic tac toe method

@blackpenredpen

5 жыл бұрын

That's my choice too.

All these methods are just one and the same method presented in four different disguises :q The first method is just a fancy way to use Viète's formula ;) Still it requires some guess work, which is bad. Especially that it won't always work (e.g. when the roots are not integers it might be quite hard to factor) :P Also, instead of just guessing the numbers, it's better to just test the divisors of the `a·c`. Similarly the second method, which just uses the fact that the common factor of 4 that can be taken out from the second parenthesis is never 0, so it is not part of the solution. It's kinda similar to factoring out the 4 from the original trinomial equated with 0, and then, since the coefficients of `x` have a common measure (4), it works the same as with integers (the same solutions, just scaled up/down). Third method, again, is just Viète's formulae with scaling up/down by 4, as in method 2. Also the fourth method can be traced back to Viète's formulas, since it has the multiplications of `a·c` and summing up to `b` in it. You know what's the _best_ way of factoring polynomials? The one in which you don't have to GUESS the factors by trial and error! :P

@blackpenredpen

7 жыл бұрын

Sci Twi I have no idea why you have no idea that I actually have that idea.

@trueriver1950

6 жыл бұрын

Sci Twi yes all of these are the same in their underlying theory. as a fact of teaching rather than a fact of maths experience shows different learners find the different visual layouts easier or harder. Good maths teachers (including BPRP) offer muliple techniques so that students can choose the one that works for them. Bad maths teachers offer only one technique and leave half their students who that technique doesnt suit believing they are too stupid. Personally none of these work for me and I use the QF instead. But when I am teaching I offer a variety of methods and have observed that only a small minority of learners like my own favourite method. BPRP of course knows these four are all rooted in the same underlying algebra - but he does not let that get in the way of his teaching skills. The student does not need to know that the technique he likes is "just the same" as the one he hates. He or she does need to be encouraged to trust his own choices among a selection of valid techniques.

@peterhemingway2264

5 жыл бұрын

I just like to call the quadratic formula the ugly completing the square method. It's all the same, but really fun to see how many cool ways you can present it to make it look better for the ones that are learning.

i am literally mind blown for the lazy ac method!! it just makes sense and its super easy!! thank you!!!!

Nothing more satisfying than the matching pair in the grouping method.

Better than Khanacademy :)

@binarytext4494

7 жыл бұрын

Kristal Kristal no.......

@Alberto-we6yl

7 жыл бұрын

Yes!

@devancornelio3340

7 жыл бұрын

totally

@zektaib1020

6 жыл бұрын

Kristal Kristal noooo

4 methods, no one convinces me, the last one was the worth (guess, guess guess...) no, the only one that always works : is to find the roots of polynomial and (x-root1)(x-root2) roots can be fond by computing : delta=b²-4ac roots= -b +/- sqr(delta) / 2a that's done. no guessig at all.

@grogcito

6 жыл бұрын

You see after practising for a while, you can recognize when the solution is nice and clean (integers) or not. These methods are intended for fast and easy solving compared to using the quadratic formula. One personal favorite is to first compute that delta to see if it has real solutions. If it does, then try out the tic-tac-toe as shown in this video with a first guess (shit works most of the times) and if it doesn't, then completing the square and then a difference of squares (skipping some trivial calculations of course). It works just as fine as the formula, and unless we have very big coefficients (which I would just undeniably use the formula) it's faster. again, we only want to solve these problems as fast as possible.

Finally a video that I understand properly. Now I can easily factor trinomials. Thank you!!

I really needed this🙏

I like the lazy AC method. I will try it tomorrow along with the tic tax toe method. I’ve been struggling with polynomials. Thank you!

Lazy AC Method for me.Thanks & more power to your show❣️

The tic tac toe method was awesome. Thanks so much for the help. Subscribed!

Your a good teacher you inspired me

Hello! AC grouping worked best for me. Thank you sire.

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.

Wow, months of trying to get this. Thank god I ran across your video!

U are amazing man u helped me for my exam amazing........ I was preparing for my exam from other KZread channel but I did not understand but u explained me ...... So thank you for that

came in clutch thank you so much

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.

Thank you so much. 😁 Slide and divide for me

This is so nice and informative as well. Thank you so much ❤️

my new favorite method is slide and divide, thanks for the video!

Great video - I think I like the Slide and Divide method the best with the Lazy AC coming in at a close second.

Thank you so much you helped me so much. I learned from you in like 5 mins compared to my teachers with 2 periods of math. (2 and a half hours.

Thank you so much you really helped !!! I have a quiz tomorrow and I feel a lot more confident

AC method plus grouping is my favorite. Thanks by thr the way this video helped

I knew the first one and the last one technique but the others only now. Thanks for sharing man.

thank you so much for this video. slide and divide helped me understand how to factor even when my teacher couldnt teach me. you saved my life!

Thank you . Way much easier to understand .