Factoring by Grouping

[TeamJordan1182]

What is : 8a^2 - 4ab +6ac-3bc ??? plz help

[cassilycassily]

I love you for posting this.

[camel04]

Patrick thanks for your videos. I am a bit rusty on my algebra and I have been reviewing things lately. I am curious as to why the method you used to solve 2x^2 + 5x + 2 works. Particularly, I am wondering why multiplying the two extreme coefficients gives you the clue for how to break up the middle term.

[iisdashik]

Thnx bro , I always had trouble doing Quads. But you helped me ease it out.

[VideoGameCowGirl]

what if the numbers within the parenthesis do not match?

EXAMPLE: 2x(1x+2)+3(1x+2+3) 

[patrickJMT]

@VideoGameCowGirl then factoring by grouping does not work

[X22689]

i get everything but the end, why is it x = -1/2 and x = -2 ???

[Meeku121]

wow i've watched many of your videos and i noticed you are left handed

[giraffesrc00l]

looking up videos on youtube on how to learn a math lesson because your math teacher sucks

[jordanwuy]

wow your handwriting is good considering that you're left handed :D

[Animega888]

Thank you very much

[MaketheMusicFasion]

Omfg I love you! I forgot this and when I came to your video you helped me remember what to do, thanks!! :)

[patrickJMT]

@MaketheMusicFasion glad i could help : )

[HdxMobs]

thnx dude u make algebre easy

[DinosaursAndLipstick]

@ 2:48 why did you put the 2?

[ivoyoyoyo]

God bless you! you helped me more than my teacher!!

[OfficialAla]

QUESTION; how do you know where you need to factor an equation completely by grouping, or by using SUM OF GROUPS etc.? that always confuses me! i never which method to use or which is more appropriate..is there anything that separates the two or makes them different?

[prettymizpah]

:)))))))



[babylamb21]

I had a quiz the other day and it had the question 4x^2+2x+9. I tried to use factoring by grouping but I couldn't find factors of 36 that added up to 2. How would I factor this??

[patrickJMT]

@babylamb21 if you use the discriminant ( b^2 - 4ac ) you will see that it does not factor.

[lorikano]

how do you factor x^2+4x+2 ? I never get the answer correct .help ?

[patrickJMT]

@lorikano you can use the quadratic formula to find the factors

[doryanishayan]

thanks a million. im studying mechanical engineering in college first year and i studied this stuff 8 - 10 years ago and i forgot everything .... this helped me a lot...thanks

[patrickJMT]

@doryanishayan glad i could help, welcome back to the world of math!

[theaddictedtomusik]

...signed in to say: "THANK YOU!!!!!!!!!!!!!!!!!!"

Bro, if it wasn't for you id be failing! You explain everything better then my teacher ever could!

[trueindianballer]

THANKS A LOT DUDE! GOD BLESS YOU! :D

[Ninjaferret666]

Thanks for the video which helped in my quick 'factor by grouping' google search, but I wish you explained how this method can be used in other situations.

[filmmetoo]

@patrickJMT Thank you so much for all your videos.

My prof gets a little over the top with very complicated explanations for simple procedures and you help clear it up.

[sweet1460]

thank you soo much i so understand u better then my teacher

[bikatakasek]

i hope this problem can do

[cazual1]

3x^2-8x-12???????

[scottrex33]

OK, I see a common mistake with these videos. The narrator just gets on a role and FAILS to Explain each step. We don't care about the first step and last step. What about the middle.

[DarklightALBANIA]

@scottrex33

Can you do it better ,This boy in here is the best at what he does and you have no right to say anything negative

[patrickJMT]

@DarklightALBANIA rule #1 of youtube: do NOT feed the trolls : ) but thanks for the support!!

[blackandwhite2015]

THANK YOU> SO HELPFUL> MAY GOD BLESS YOU WITH MORE WISDOM

[Scrunchy51]

This NOT How i learned it

[ninjapharmacist]

@Scrunchy51

If you're trying to say something negative here, guess what? You're a fool.

There are different ways to do algebra. Just because you know one way, it doesn't mean it's the correct way.

[ninjapharmacist]

@ninjapharmacist

*the only correct way, I meant to say.

[Scrunchy51]

@ninjapharmacist

Dude your assuming i said something negative.

I'm NOT a fool, in which you were the one being negative.

Uh thanks

[bchisenhall]

This question was asked a couple times with no answer. On the second example, why is x = to negative 1/2 and negative 2? If it's a long answer, is there another video that explains that part? Also, is there a video that does a good job of explaining why the simplifying process works the way it does? For instance: Why is 2x^2+4x simplified to 2x(x+2)? I know to do this and can come up with the correct answer, but I don't understand WHY this works. A link or a video would be awesome!!

[bchisenhall]

Ok, It seems so obvious now that I've actually figured it out. Feel stupid for asking it but glad I got the answer. I'm not the best at explaining steps but I'll try in case anyone else has a similar brain freeze on this.

In the last step, you have (2x +1) = 0. You have to minus 1 from the left side of the equal sign and minus one from the right side of the equal sign. That gives you 2x = -1. Because -1 is the product of 2x, you have to divide 2 from both sides. That gives you x = -1/2.

[X22689]

@bchisenhall thank you that explained my confusion!

[Michiganskateboard]

youre a gnarly guy

[thecam4444]

nothing like craming for exam wtachin this guy yur awsome

[Nooreazy]

you are a god amongst kings my freind.

[brozac1011]

How bout binomials

[brozac1011]

Is it ok if u interchange the broken numbers

[Soccer4life961]

god bless you

[MsJokert6]

Left handed people are smart.

[thecapone45]

@MsJokert6 lol! omg, ive been watching his vids for so long and i just now noticed he writes with his left arm,,, wow, lol.

[dazzlingD9296]

what if u have a binomial? for example:

36a^4 - 4a^2

[mcorleone141]

thank you so much bro

[fahoood111]

Thank You ! Good Job ;)

[osvideosdojoao]

Look at this:

12x^5+6x^3-2x-8

is this polynomial factored by grouping?

I've tryed without success.Are there other ways to factor this?

Thanks

[naillover25]

thank you so much i was way lost with my home school program

[Bouncertt]

I love you man...

[dallasfan24bossman]

Thank you so much. My teacher is smart, but cannot teach worth a flying fuck. You have saved by ass.

[OutDoorsExpertiece]

I love you.....

[mkd753]

This is a great video you put together! I post this video on my google website for my students to watch at home if they need additional help, because I teach factoring the same way. I like that this works 100% of the time, as long as a polynomial is factorable. Thanks again!

[chocolatebunnynick13]

He's wayy better than my Alg teacher -.-

[EbonyHairedPrincess]

Finally! Thank you so much for explaining the steps clearly. I may just pass pre-calc after all.

[blastdude12]

How advanced in calculus are you PatrickJMT?

[BeansInABottle]

I was pro at factoring last year but unfortunately forgot most of it and so this was a much needed refresher...thanks.

[TheHofilmfan]

what about something like 32x^5+y^5?

[MsRhonda01]

u r da best =)

[MsRhonda01]

u r da best =)

[VJDJPJ501]

my problem is 4x^2-22x+10 and its not working out right

[youngindian]

i am extremly thank full man u saved my life

[omshark900]

Would this also apply to x^2 - 4x + xy - xy?

[patrickJMT]

@omshark900 well, the last two terms of that just cancel out... leaving x^2 - 4x when u just factor out the 'x'

[omshark900]

I like your marker. :)

[evry1scritic]

I have a question, how would you factor 15x^4y^2+6X^2Y^2

Would it be by grouping?!

[jsobiranski]

@evry1scritic Yes, factor by grouping means we take out the common factors in each term. Therefore, the first term and the second term both have (3x^2 y^2) in common. Thus, we factor out (5x^2 + 2) from the second term.

Therefore, we get 15x^4y^2+6X^2Y^2 = (3x^2 y^2) (5x^2 + 2).

[mcna0138]

wowwww you just made that so much easier, thank you!

[NasaPayag]

man i u really helped me a lot. hope u stay bcoz i still have lot that i want u to help me in TRIGONOMETRY" thank u thank u thank u i deserve all the credit

[gottalovedamon]

im in 10th grade and this saved my life! thanks,

[sasha1185]

i understand this video, im in middle school and i just got my classes switched and my math class is what is similar but looks difficult, for example 49x^3-35x^2+56x-40. now we dont have to solve them, just give the formula without the answer. this for me is only algebra, i can imagine algebra1 and im only in 8th grd.

[FEARxAIRSOFTxTEAM]

video on factoring a trinomial?

[shebna12]

i think there it costs some time to get the answer

[lilvic777]

man ure the best! u saved my life..im failing math and with this im gonna get an A ;D

[Triumphit1]

8x^2-6xy+20xy=15y^2

Factor by GROUPING?!?!!?

[patrickJMT]

@Triumphit1 looks right to me

[Triumphit1]

@patrickJMT You helped me pass my test today, truly thanks

[patrickJMT]

@Triumphit1 sweet, congrats to you

[guyfootballfan]

I luv what people like you are doing, it just so helpful. Keep up the good work.

Carzeeladie is right, you deserve a endosement by sharpie.

[kushprez]

yo mi boss dis help mi wicked enuh,

[crazeeladie]

dang i can't believe i forgot how to do this, thank you!! you deserve to get sponsorship from sharpie :D

[kakakarlyn]

test tomorrow and im freaaaaaking.

i seem to be understanding ! THANK YOU

[Chichiri520]

My textbook calls this type of factoring (exclude the = 0) ax^2+bx+c. If I multiply those terms you did in the beginning, can I always factor the result? The reason I asked is because I worked with the same method but it only worked if it was x^2+bx+c.

[Georgi74]

why do we have teachers? we just need youtube, its free and better

[batistaker123]

Ok I'll be honest I have a good teacher but I don't pay attention in class everyday..

Your videos help me a lot, thank you. Wish me luck on my test tomorrow!

[NotAboveAverage]

You deserve to be a partner. Thanks

[callmehiphop]

i wish you sat next to me in math

[darkknight302]

my teacher goes too fast and makes no sense. this really makes things clear!!!

[tonyjohnston01]

i just learned more on this video than in class. thank you for breaking it down

[patrickJMT]

@tonyjohnston01 u r very welcome

[miguel1waterpolo1guy]

thank you so much man your good at explaining it

[Hockey02ful]

u just made me get a 98 on a test ur the man and u saved my life

[patrickJMT]

@Hockey02ful u took the test, not me! : ) good job!

[carllambitco]

thanks for your tutorial.. :)) it helped a lot :)) keep up the good work man... way to go!!

[stopnope]

got an exam tomorrow on this,thanks for the help! :)

[patrickJMT]

@stopnope good luck on your exam!!

[kingofdice66]

what about 3x^2+16x+5

[Deadly235]

I don't get the last step. right before coming up with the answer. argh

[misterogie]

i dont get the last part how's that became -1 half?

[ProjektLament]

Yeah those are easy, how about a^3+a^2b+a+b / 9a^3+9a

[Jamiecool80]

wow, it was like 3 weeks of maths class in 9 mins CHEERS!

[DavidAlexanderLopez]

LEGEND!!! 

[PicalilyProductions]

Thank-you so much! You have no idea how grateful I am! I have never got quadratic equations with a coefficient of X squared and now it makes so much sense. i'm wondering why I spent all those maths lessons confused!

[arioch467]

um i just love you. thats all.

[Melatelo300]

perentasis waaaa??

[DavidAlexanderLopez]

@Melatelo300 Brackets, it's what Americans call the brackets

[Melatelo300]

@DavidAlexanderLopez

ok then......... Weird. Why make it such a complicated word for it when u can just simply say Brackets

[loudmouth346]

THANK YOU SO MUCH!

[smurphlikesgreen]

how does "x" = to negative 1/2?

[arioch467]

dude, i love you. its that simple. youve saved my butt too many times.

[chuapf]

There's a formula to this right ? Isn't that easier and faster ? ;]

[munchc]

Very helpful i totally forgot how to factor

[roflcopter2225]

thanks, sometimes you forget even the basics like this when solving more advanced stuff.

[mrhensonandmrhartzog]

I love you, in a completely nonsexual way

[opps2341]

I think all teachers should do this you saved me extreamly helpful

[14Chiquilla]

ok i got all most everything exepts i do not under stand the part where u have to factor out... u brek down the 6? and or i don"t know.. i don"t know where the

3x (2x-3) -4 (2x-3) come from or how u do tha?

[sportsboy4]

haha i think this is soo cool how you post videos on youtube for your students. smart man. (especially because most kids today are on the computer all the time) thumbs up. wish my teacher did this but your videos are awesome ahah

[phodem12pm]

you saved me! tmr i have test

[carolinesunshine69]

Just so you know, you just saved my life:] Thank you so much, you're my homeschool teacher and you dont even know it:D

[patrickJMT]

@carolinesunshine69 ha, happy to help!

A+ for you!!

[Noobtender]

I'm just learning and I dont understand how to do problems like 2ab-6ac+3b-9c, and thats just #3. It would be really helpful if you could message me or make another example video of more advanced viedeos. Or if anyone could message me a solution, much appreciated. Great video thanks.

[chikitomybabi]

you helped me for several of my homework problems but im having trouble with this one that doesnt work like the other ones you did: 7j^2-30j+8

[SammieW23]

i dont understand how you got the answer that is in parentheses in the examples you used....

can you explain it.

[MrScoop1994]

Thanks! I am in college and my teacher sounds like blah blah blah when she talks. i always come here for help

[af4lazn]

thak you thank you this helped alot thank you

[xXWolfpyreXx]

Thanks, eatme690808 ^^

[SunshineMyHeartLove]

OH MY GOD!!! I love you!!! You just saved my life!! I had no idea how to do my homework so I look it up and Whala, you're video taught me better than my teacher did!!! Man, You're my hero.(:

[xXWolfpyreXx]

Wait... I could factor out the 4g, yes?

[eatme690808]

Break it up into two groups: (7g^2 + 7g) - (4g + 4)

Factor from there. Hopefully it's obvious what the two groups of ( ) have in common.

[xXWolfpyreXx]

I can't factor out my new equation

7g^2 - 4g + 7g - 4

HELP

[Blak433]

bad teaching.. your just blurting out random steps without any reason what so ever.. Why?? i ask you, why??

[lafyguy]

thank you

[nobodypickthis]

what if its a cubic or quartic?

[DeRealUno]

that seemed like decomposition.

[yyttr4]

What if there is no middle term! S: x^3-4x^2+2x-8

[cdilJ]

factor out x^2 from first two terms. and it will give you x^2( x - 4) and 2 factor out from last two terms and it will give you 2(x - 4). So you will have x^2(x - 4) + 2( x - 4) = (x - 4) ( x^2 + 4)

[dltmdgn]

If you guys want me to show you a simpler way of this problem just subscribe to me or send me a message and i can show you an easier way. Another way to solve these problems is to go to youtteachermathhelps and get help from there. They are really helpful and most of those teachers are quite experienced and smart.

[andrewtrucker]

ok but you are going way too fast!

[theGTAexperience]

when will i ever use a variable in a real life situation? I wouldn'rt solve it mathematically thats for sure I'd use logic or common sense to solve it in the easiest way, not by setting up some complicated formula and equation that will waste my time, paper, and led/ink

[theGTAexperience]

when i need to find out how big something is that I ordered I will read a box, label, I might call the company... but I'm sure as hell not going to break out complicated geometry formulas to figure out something in a much more complicated way... need I list more examples? i have a bunch

[theGTAexperience]

no, please explain to me how I will use VARIABLES in a real life situation rather than logically using common sense to my advantage, outside of school, or can't you?

[theGTAexperience]

stick to one part of mathematics, VARIABLES you keep changing the subject, either that or you're just that ignorant and your skim reading three lines of text... i will never use variables in my life, i know I won't because i have the common sense to know that If I need to find something i will find it without using variables because there is no need, if i need to find the weight, length, mass or volume of something i will use instruments rather than do some complicated formula and waste my time

[theGTAexperience]

lengths can be measured using other devices and tools same with angles physicist I'm not to sure wtf a quark is so i'll leave that alone.

[theGTAexperience]

i meanta situation that I'd be in but ok think what you want the fact that you assume I'm not from college and that you think that being in college magically makes you smarter (and yes i realise you can but for others, not so much...) proves your level of ignorance oh and try to delete all of them next time ;)

[123MrBee]

You are learning this so you can prepare your brain for more abstract concepts, which by and large make you more valuable to an employer, due to your higher skill levels, in whatever job.

Who do you think will earn more in their life? A person who has prepared their brain for learning, or someone who says learning is useless (and likely not willing to learn)? Who would you hire for your business?  This is a major thing to consider - very long term. Please consider the long term.

[missrandom80s]

calc. . . thats why im here

yes! i understand it!

[choklette]

Augh. I'm having to take algebra again for the first time since I was 13 (because I didn't bother getting my liberal-arts-copout math credits at ACC, actually) and was suffering the WORST mental block about factoring.

It makes perfect sense after 3 minutes of this video.

I love you forever now.

[MusaAsif]

thank you so much for this video. what grade do schools normally teach this stuff in? cuz im in college trying to get into calc 1 and i was never taught this method of factoring.

[missychino]

In my high school, we learned this in Algebra 1, (for me) 9th -or-10th grade.

[aceofhearts157]

8th grade and 9th grade

[Transmedal2]

In the part in first equation you did, you grouped the problem into two parts 2.49

why did the 4x become a 2, that is where I am having problems.

[olansaster]

he basically factored out 2x from 4x. bcos 2x is common to both 2x^2 and 4x. making 2x^2 + 4x into 2x +2.

[GuyKyle87]

you have 3 parts to the equation, a + b + c = 0, all your doing is getting what you just worked out and putting that as b.

[cookinkyle]

This was EXTREMLY helpful. This never made sense until i watched this video.

[vall3ygrl09]

MathMikie, factoring is always the preferred way to solve a quadratic equation. Completing the square or using the quadratic formula are usually much more involved.

[lax800]

my math teacher teaches this stuff way too hard and complicated. thanks for the help

[fmanaruto]

wow dude this is so dam helpful

thnx