Factoring Quadratics - The Cross Method

[@aungheinkhant-zemusashi3517]

This video is everything I need for the maths exam. THANKS!

[@MisterBrash]

Happy to help! Share it around.

[@brandonfeng5416]

Wow, thank you so much. I was taught this a year ago but forgot how to do it, and was completely confused seeing other tutors break up the middle term. This makes things 10x faster.

[@loganmcfarland4982]

This is super helpful, I completely forgot how to do this and now I remember, thanks!

[@MisterBrash]

Happy to help! Spread the word about my videos!

[@komaljeetkaur2862]

i had initial doubts regarding sign but all thanks to yu .All doubts cleared ..... Grt vdio. ..keep it up

[@anglez8044]

Thank you so much. This video has helped me make it way easier to calculate quadratic trinomials!

[@ruller8901]

Thanks for this, I missed the first like 3, 4 weeks of school and everybody else was taught this last year and I never understood how to use it.

[@_sindiswa]

this this, sir, i owe you my math marks❤

[@ruchi5696]

My saviour THANKYOU 😭💗

[@dawoodsada835]

this video helped me a lot thank you

[@DailyChallenges904]

3:30 New meaning of wtf: what the factors Edit: P.S. very clean and neat videos! Thank you :)

[@Christofxzsc]

THANK U SO MUCH I GET THIS MUCH EASIER THAN MY TEACHER😭😭🙏 VERY HELPFUL FOR THE TEST TOMM😭😭

[@zDefaultX_quit]

SAME MINE IS ON WEDNESDAY GOOD LUCK

[@manasvi9717]

thanks for the help! i was really confused at first

[@MisterBrash]

My pleasure! If there's a video you'd like me to make, let me know.

[@kianlavin]

I needed this, thank you so much😊😊

[@MisterBrash]

You're so welcome! So glad it was useful. I'm actually surprised how many views it's getting.

[@tyfirsching5379]

Great job!

[@theneochickens]

Huge respect I needed this

[@thisarmywillalwaysstay8277]

Thank you so much for doing this video it was extremely helpful.

[@MisterBrash]

Glad it was helpful! At some point I hope to have more time to do more videos.

[@mr.heisenberg5119]

Thank you Sir 👌👌👌 outstanding class 💯 you desese more subs

[@salehajabeen196]

hello sir do you think we will get marks if we do this ... i mean what about the working ?? and this doesn't apply for roots right? apart from it thank you for this :) it'll be really helpful for me if you answer this

[@MisterBrash]

That will depend on your teacher. Is the goal to show knowledge of factoring (ability to get the correct answer) or is the goal to show specific steps of a specific method? That will depend on who is grading you and what the goal of the assessment is.

[@TienShan3.14]

If you need to show the steps, all the products of x terms that MisterBrash showed (ie + 21x + 4x in his first example) are just breaking apart the middle term of the trinomial. Once you have it broken down (12x^2 + 21x + 4x + 7), you can just go through common factoring to get to the 2 brackets of binomials.

[@aryamansingh3606]

Thank you my math teacher is teaching this method and she thought it in a different way

[@thamkeyki8835]

Thank You so much! Helpful!

[@Yourcutie-e2v]

Thanks you, your was very helpful

[@eliemitoumba-tindy1663]

Thank u so much. Very helpful

[@BoofGalls]

in 6:27, do we just forget about the negative sign in front of the 6? Does it not matter? (in the equation, not the answer)

[@MisterBrash]

Sorry it took me 4 days to reply! Didn't see the notification. The negatives in the equation will help decide where the negatives go in the answer but when you are setting up the framework for the answer you do it without negatives at first. Then, you look at where the original equation has negatives and you figure out where they have to go in the answer. Watch that portion of the video again - I start without any negative signs when I'm playing with the answer. Then, I take a look at -13x and try to figure out how to get a negative there AND have a negative on the 6. It's scrap work. I should also mention that this method isn't exactly "mathematical", it's more of a trick. I hope that makes sense!

[@s-megagaming908]

Thanks for helping a Lot, many of the books doesn't completly explain the cross method THANKS!!

[@MisterBrash]

You're very welcome! Glad it could help. There are many ways to factor these kinds of trinomials and people have personal preferences about it.

[@Ihavefever]

are there any factorising methods that are quicker for solving this type of equation..? great video btw :)

[@MisterBrash]

Absolutely. This one is sort of a guess and check method (and TBH I don't really like this method). I only made this video to demonstrate that it exists. The product & sum method, which goes by many names, the decomposition method, the fraction method, etc... And when all else fails - the quadratic formula.

[@Ihavefever]

@MisterBrash I see, thank you for sharing.

[@TienShan3.14]

FINALLY! I have found another educator properly explain the cross method. I learn this years ago and now I am teaching students how to do it properly. I actually list out all the factor pairs of the leading coefficient & constant term (the a & c terms), in the ax^2 + bx +c format. That way, my students don't have to recall which pair they have (or haven't) tried. I also teach them to pare down the factor pairs (ie, skipping over a pair of even factors if I am looking for an odd sum). They can also systematically exhaust all possibility and say the trinomial has no rational roots before they see the quadratic formula or the discriminant. Here is my attempt with 55x^2 -373x + 630 kzbin.info/www/bejne/gYjNap6FZqp8oqs

[@teacherasmith]

Is there ever an instance where the factors of the first number and the last number don’t work out to give us the middle number? What method could we use then?

[@MisterBrash]

Absolutely, that can happen. In those cases, it's not factorable and you'd have to use the quadratic formula to solve for the zeros. We call those "not factorable".

[@koalamm2]

THANK YOU

[@xuan20008]

omg u saved my lifeee

[@edmundlee1218]

Is this method only guess and check or is there an algebraic way to do this

[@MisterBrash]

This particular method is not very "algebraic". It's a trick. If I recall, I mention that in the video but maybe I don't. I had a few students ask me about this method so I made a video on it. There are more algebraic ways to factor these kinds of equations. Here's my videos on factoring monic trinomials: kzbin.info/www/bejne/kIrTkneLor5sqcU and non-monic trinomials: kzbin.info/www/bejne/a16ap4Vpbbp7n6c There are other algebraic methods as well.

[@TienShan3.14]

List out all factor pairs of the leading coefficient, as well as the constant term. Then you can go through all the combinations of factors until you find the one that will produce the "middle terms", the 2 terms that adds up to the linear terms.

[@pakistanzindabad2217]

thanks

[@Charlotte-th7pt]

Thank u

[@JustNeutral]

so its guess and check, no other way to not guess? :] ive not rlly tried tbh, does the guessing not take that long as i think it is? nonetheless, tysm!

[@MisterBrash]

There are other methods that are less guess and check. This particular one is not my favourite, I was just asked to make a video about it. I highly recommend you check out "decomposition" for non-monic trinomials.

[@AfoS19]

Don’t we distribute when we get our numbers in the parentheses?

[@MisterBrash]

That would be expanding, which gets you right back to the original question. Expanding (or distributing) is the opposite of factoring. The goal here is to determine the factors.

[@apunene8981]

what a legend

[@Kyaw_Htet_Aung]

If -2x²-x-3=0 then can we apply cross method?

[@MisterBrash]

No because there are no real roots to that equation. So no method of solving will work unless you use imaginary numbers.

[@fiorellagarcia6382]

can you do it for 2x^2+8x-8? im stuck

[@MisterBrash]

Aside from the fact that there is a greatest common factor (GCF) of 2, making it 2(x^2 + 4x - 4), it does not factor any further.

[@megalavelu4854]

How do we know where to put the negatif?

[@MisterBrash]

They need to add to the middle term. So if the middle term is -3x you need the two values you come up with to add to a -3x. Let's say those two values are 8x and 5x, the only way this can happen is if the 8x is negative. From there - you go back to how the 8x was created and place the negative on the value that created the 8x. Take a look at the video again at a time of 4:07 and you'll see I show how to decide where the negative should go.

[@MisterBrash]

And again at 6:20

[@hazzaftw912]

What would you do if A was negative?

[@MisterBrash]

You have two options: 1) Factor out the negative from the entire equation/statement first (so all the signs change and the final answer has a negative in front). This would be my first choice. 2) The same process, just place the negative on only ONE of the first terms. But you bring up a good point, I should have included that in the video.

[@auntmaysbajanpeppersauce359]

the method doesnt work if the first number as well as the last are both prime

[@MisterBrash]

Sure it could. For example, 7x^2 + 20x +13 = (x + 1)(7x + 13) or another: 19x^2 + 438x +23 = (x + 23)(19x + 1) Obviously it won't work for situations where the trinomial is not factorable.

[@zyphen665]

The first and last digits are 2 and 3, both are prime numbers and the middle number is 7, doesn’t work

[@MisterBrash]

Sure does... The middle number (7) can be represented by 6 + 1. If you take the first term of 2 and use 1x2 and the last term of 3 and use 3x1 you'll end up with a cross that creates (x + 3) and (2x + 1). Hard to describe in a textbox.

[@zyphen665]

@@MisterBrash Thank you! At the time of commenting I didn’t really understand the method, now that I do it was a silly questions haha 😅

[@dawoodsada835]

i subbed

[@litobeatz639]

I wish I had u as my meth teacher

[@MisterBrash]

Sorry but I don't know much about chemistry.

[@KoreaNumberOne]

Katie Sorensen, leave a like if you ever come across this video

[@chocolateangel8743]

This is not a trick. It is reverse double distribution.

[@MisterBrash]

Right, but if I called it that teenagers would run for the hills. By calling it a "trick" they go "OH THAT'S SO EASY".

[@chocolateangel8743]

@@MisterBrash Ohhh....I was never like that. When it comes to math, I've always been one of those people that needed to understand the mathematical logic behind what I was doing in order to properly execute any algorithm. I don't do math by memorizing steps.