How to use the quadratic formula to factor trinomials: 👉 kzbin.info/www/bejne/fJzdf4Wwh7OJZqM
@jimhaskell54856 ай бұрын
I've been a math teacher for 29 years, and I've never seen the "slide and divide" method. Love it!!
@shauryadivya17366 ай бұрын
Can you explain sir why does it works?
@chocolateangel874324 күн бұрын
It's been very popular for the past few years.
@ndrslvn18866 ай бұрын
I prefer the first method because it doesn't require any "magical" steps, just basic algebra.
@D17D6 ай бұрын
Here because I'm a first-year CS student and I forgot how to solve a quadratic
@patolol30916 ай бұрын
😂😂 probably me in the future
@tobybartels84266 ай бұрын
I always do the a-c method, because it's systematic; there's no trial and error, just going through a list of divisors. Plus, if it can't be factored, then you'll know it; you won't worry that you missed an option. (Generally I do a-c by grouping, to not introduce new elements, although the box is slightly faster.)
@ivannovalery65046 ай бұрын
I usually teach the final method like this ( a + c) | bc ( b + d) | ad ----- -- + 6x^2 - 3 |+7x a and b are factors of 6x^2. c and d are factors of -3 Cross multiply these factor to get bc and ad. add them together and use +7x to check if your selection of factors are correct
@ASChambers6 ай бұрын
It’s always nice to see different ways to solve common problems. Thanks for sharing.
@johnroome55474 ай бұрын
I normally use the Factor Theorem, where if f(y) = 0, then x-y is a factor. Can be difficult because you sometimes need fractions, ie f(y/3) = 0 means 3x-y is a factor. You also have to use substitution and poly long division, but it’s a satisfying method and works for polynomials of all orders, not just quadratics.
@elliekittymeow6 ай бұрын
If you show this video to twitter users they will literally explode. Also, you're a great teacher, thanks a lot!
@schlingel00176 ай бұрын
I think first method makes most sense. It is also very easy.
@nathanbarnes39696 ай бұрын
The best method is not any of these 5, or the quadratic formula. Completing the square is goat
@tanelkagan6 ай бұрын
@bprpmathbasics Great video as always, but a few observations:- 1. In Method 1 - AC with grouping - having found two numbers that sum to 7 (being -2 and 9) you say "if one of the numbers is negative, write it down first". I can't quite figure out why that's important. Clearly in step 2, if you were to write instead 6x² + 9x - 2x - 3 this becomes 3x (2x + 3) - (2x + 3), which again factors in exactly the same way to (3x - 1)(2x + 3). I haven't tested many cases, but it seems to me that if the quadratic *does* factor in a nice way like this, then it won't matter how you group, you'll always get the same result. It links to Method 2 - all that's happening is that we're either grouping "across rows" or "across columns", but either way should work equally well, right? Do you have a particular reason for wanting to write the negative number first? 2. Purely my opinion, but Method 3 (the "weird" AC method) and 4 ("Slide and divide") would seem to involve more things to remember, and more things that could go therefore wrong. They're probably not methods I would recommend to anyone that isn't already very familiar with factoring - are there cases where these methods are easier to use? 3. In Method 5 ("Tic Tac Toe") - you say "We ask ourselves 'what times what will give us 6x²?' and the correct combination is 2x and 3x". Well, that is *one* combination, sure, but the reason why it's the *correct* combination is rather much glossed over. As a beginner, it's not obvious, and I think it would be useful to establish why you've rejected the combination 6x and x. In other cases, there might be three or more combinations (eg. 12x² might be factored to x and 12x, 2x and 6x, or 3x and 4x. Of course the wrong combination is not going to work as you progress through the method, but in your example if you were merely selecting 2x and 3x because you already knew the answer, that obviously wouldn't be a valid approach for someone looking at the problem for the first time. Thoughts?
@WilliamMarkRock6 ай бұрын
I forgot the one I took at school but I also didn't like any other method because they didn't seem familiar. The one in the school textbook was different from the one that was explained by the teacher, and I couldn't understand it. This one has both, plus other methods I found on the internet, and it explains them all very well. =
@teengrogu51776 ай бұрын
I love the 4th and I know why it works always
@lumina_6 ай бұрын
I've always done the "weird AC" and I've certainly always considered it weird, but I'm super used to it haha
@ZipplyZane6 ай бұрын
Yeah, I don't like the last method because you now have more things to check. You have to check all the factors of a *and* all the factors of c, mixing and matching. Discovering the first method was a revelation. It works. If I can't do that, then I use the sixth method: the quadratic formula. If I actually need the factors, I can reverse it from the answer, eg. if I get x=3/4 as one answer, then one factor is (4x-3).
@jeffw12676 ай бұрын
I would just use the quadratic method, if the factors are not immediately apparent. This one can be done mentally if you know that the square root of 121 is 11.
@bprpmathbasics6 ай бұрын
the pq quadratic formula that they don't teach you in school kzbin.info/www/bejne/hJ27kImIYsprp9E
@lookingforahookup6 ай бұрын
They do teach it. It's just that the teachers don't want to teach.
@anuragguptamr.i.i.t.23296 ай бұрын
I would rather always prefer method 6 (the quadratic formula). Because it works in all cases, such as the cases of irrational roots or complex roots.
@AzureKyle6 ай бұрын
These are all interesting methods, however the last method is the one that's closest to what I usually do. I don't use a tic tac toe grid, I just look at the x^2 and ask what times what equals my x^2 (in this case 6x^2) For this problem, I'd get x and 6x, as well as 2x and 3x. Then I'd look at the -3 and get either 1 and -3, or -1 and 3 Then I'd make every combination of the factors ie. (6x+1)(x-3) etc. and then using FOIL, solve each one until I got the original problem (in this case, (3x-1)(2x+3)) However, I might utilize the first method from now on, as that seems the easiest one to do.
@jimbobago6 ай бұрын
This sounds like an exhausting, tedious slog. 12x²-7x-12 for example has, by my calculation, 18 potential combinations of binomials to be tested.
@AzureKyle6 ай бұрын
@jimbobago Yeah, it can be, but I also enjoy working with numbers, so it's fun in it's own way.
@jimbobago6 ай бұрын
@@AzureKyle Who am I to argue with someone who finds math fun in its own way?
@ezequielgerstelbodoha9492Ай бұрын
I remember cracking my head with the weird method that was the only one my teacher used in school. If I just knew there were much easier ways to do the same
@JubeiKibagamiFez6 ай бұрын
I definitely like the tictactoe method the most. Just a question, are we solving for X?
@charleskrueger55236 ай бұрын
Not solving. Just factoring. If this was part of an equation, you would need to factor prior to solving for X.
@JubeiKibagamiFez6 ай бұрын
@@charleskrueger5523 Ah, okay.
@darranrowe1746 ай бұрын
Also, factorising and solving are essentially the same. (3x-1)(2x+3)=0 3x-1=0 or 2x+3=0 3x=1 or 2x=-3 x=1/3 or x=-3/2 x=1/3 or x=-3/2 3x=1 or 2x=-3 3x-1=0 or 2x+3=0 (3x-1)(2x+3)=0 If you know how to, factorising is normally the fastest with whole numbers or easy fractions. CTS and the formula tend to take longer due to the algebraic manipulation.
@JubeiKibagamiFez6 ай бұрын
@@darranrowe174 Oh, okay.
@bprpmathbasics6 ай бұрын
All you need for know for factoring polynomials: 👉 kzbin.info/www/bejne/b4bEoqalYpmKbJY
@hammadsirhindi13206 ай бұрын
Is there any numerical method available to calculate gamma function of non analytical numbers like (1/3), (1/5) ?
@prathmeshgaonkar80266 ай бұрын
I'm accustomed to the first method
@armanavagyan18766 ай бұрын
Last one is the best way🙏
@RatulBiswas_is_op6 ай бұрын
I think , sticking one method and fully mastery it is the best .
@ActualDumBatcha6 ай бұрын
4th is the best method by far.
@MrFrmartin6 ай бұрын
agreed
@RoniRonkoKovatch6 ай бұрын
Regarding the tic tac toe.... what times what equals 6x^2.... 6x * x 3x * 2x How do you know if to check 6x and x or 3x and 2x ??
@jimbobago6 ай бұрын
You don't. This method is full of nothing but trial and error. 12x²-7x-12, to look at another example, could be x & 12x, 2x & 6x, or 3x & 4x. Likewise, the constant term could be 1 & 12, 2 & 6, or 3 & 4 and each pair of constants has two combinations of plus/minus signs. By my figuring, this means there are 18 combinations of binomials you could form to try to find the right combination. To me, it seems like the most inefficient choice.
@donq44836 ай бұрын
My algebra teacher taught us the Amazon Prime way, but this was in 2005 long before Amazon Prime became what it is today 😂
@bprpmathbasics6 ай бұрын
😂
@potentialofprotonis36 ай бұрын
me seeing the given question- :DD me then seeing bprp's shirt- 😵💫😵💫 i am in 8th and know nothing about calculus lol
@Newscrews106 ай бұрын
Many years, many students...Box method easiest for them to use and remember. I teach all of these using a diamond method and the Box method can be used with least amount to remember. They do mot have the stamina to guess and check anymore. I had to change from guess and check after so many were getting frustrated.
@tkhcheng6 ай бұрын
Which method would you use for 10x^2-57x+54?
@bprpmathbasics6 ай бұрын
Tic tac toe. (5x-6)(2x-9)
@tkhcheng6 ай бұрын
@@bprpmathbasics Does that mean this method is the most versatile?
@ahadshaikh3686 ай бұрын
You can also use formula method which is equal to [-b+-sqrt(b²-4ac)]/2a
@richskater6 ай бұрын
The video was on methods for factoring, not solving.
@newaccount-cz6tb6 ай бұрын
Factoring out is way quicker almost every time than formula. It is only troublesome when you get factors in roots and fractions
@tobybartels84266 ай бұрын
@@richskater: Although I wouldn't recommend it, you _can_ factor by solving. If the solutions are r and s, then it factors as a(x−r)(x−s). If r and s are integers, then you're done; otherwise, their denominators will be factors of a, which you can distribute. (Of course, if r and s are irrational, then it won't factor.)
@jimbobago6 ай бұрын
Tell me you don't understand the point of the video without *saying* you don't understand the point of the video.
@ahadshaikh3686 ай бұрын
@@jimbobago yeah i know. It's about factorizing with different methods taught us in 6th grade.
@박강현-k9k5 ай бұрын
ari gatou math sensei
@Zevoxian6 ай бұрын
Hmm I kinda like the first (or first three) methods. I always just go to quadratic formula when a=/=1
@brendanward29916 ай бұрын
I usually use method 6: trial and error until I finally stumble across the solution.
@FleckerMan6 ай бұрын
What does common factor mean in the screen-text?
@FleckerMan6 ай бұрын
as in 2x^2 + 4x + 6 = 0 would need to be reduced to x^2 + 2x + 3 = 0 first?
@michaelmcclellan53456 ай бұрын
Have you taught the method taught by Po Shen Lo?
@alexmorgan29186 ай бұрын
Those are legit!!!!
@HarisRehmanGG6 ай бұрын
My teacher calls AC 'Product Sum', where you find ax²+(m+an)x+mn
@julzborgy3456 ай бұрын
just complete the square yall x
@monics_086 ай бұрын
I love maths❤
@ghostmelon646 ай бұрын
Mathmagical!!!
@MrFrmartin6 ай бұрын
I used the 4th way to factor which i found to be the easiest.
@robotrock32716 ай бұрын
For C, that doesn't work when you can define the smallest non zero amount.
@anuragguptamr.i.i.t.23296 ай бұрын
I would rather always prefer method 6 (the quadratic formula). Because it works in all cases, such as the cases of irrational roots or complex roots.
@YukiRisu-j9c6 ай бұрын
I LOVE YOU SOOO SOSOOSO SOOOO MUCH THANK YOU SO MUCH FOR THIS IM SO GOOD AT MATH NOW I WENT FROM 0% TO 88.9% THANK YUOU LORD AD SAVOURS
@Fatmuffintart6 ай бұрын
not even 89%?
@YukiRisu-j9c6 ай бұрын
@@Fatmuffintart I'm just better than you
@bprpmathbasics6 ай бұрын
Happy to hear and love your excitement! Keep up your good work!! 👍
@ahadshaikh3686 ай бұрын
First one is the easiest method.
@maheshkushwah84146 ай бұрын
-(-2)= +2 but why
@syedmuhammadaqil19986 ай бұрын
First
@pulkit9356 ай бұрын
Or you can just use quadratic formula
@Steve_Stowers6 ай бұрын
The quadratic formula isn't really a way of factoring a trinomial. Although you could work backwards from what it gives you to figure out the factors.
@pulkit9356 ай бұрын
@@Steve_Stowersyes, you are right, i thought you will get the same factors if we divide the whole equation by 6, but the factors you get by quadratic formula are 1/6th of the actual factors And as a maths student I am really embarrassed right now
@KermitSF6 ай бұрын
@@Steve_Stowers it is one💀. You only need one of the zeros and then apply ruffini bruh
@mikejackson198286 ай бұрын
Not first.
@GikamesShadow6 ай бұрын
I am 31 Why am I sitting here acting like a student????