Synthetic Division - Example 2

[TehRealViewer]

Writing left handed on a dry-erase board is difficult :P

[zanderg11]

what if I'm dividing by 3b-2?

[TheJoker2357]

thqank you soooo much dude also if you could post something about why it works because my teacher wants a description of it. my email is isikaku24@yahoo.com thanks

[Gunnerbudde3]

wat if the denominator of the fraction is say (x+3)-(x+5)? how wud u do the division then?

[ShankOcarinas]

Thanks for the help!

[chapinero017]

how do u find a factor for ur 3rd or more degree equation if its not given? so the remainders = 0

[geeksquadof1]

Thank you for helping me!!!!

[antiplayer99]

You sir. Are a BOSS.

[bettycrockercandles]

THANK YOU OH MY GOSH YOU ARE GOING TO HEAVEN!

I CANT GET MY PERMIT UNTIL I HAVE A DECENT GRADE IN MATH I THINK I JUST FOUND MY NEW TUTOR :)

GOD BLESS YOU<3

[jerrahwal]

i love him

[Noni136631]

Thanks man if it wasn't for you I would be failing pre-calc!! Why are you so smart??? I'm jealous

[patrickJMT]

@Noni136631 i worked my ass off. people seem to think that i was just born with all of this knowledge : ) it did not quite happen that way though. WORK PEOPLE, IT IS CAUSE OF HARD WORK!!!

[zigyy553]

How would I do it if I'm dividing by a fraction, like 1/2? I feel confident in most others, but the fractions...ugh.

[TigersEatEmos]

What would you do if the x to the fourth, would have had a coefficient?

[patrickJMT]

@TigersEatEmos i would have used it, instead of a 1

[raystrife234]

@patrickJMT how about if your x to the 4th is a coefficient and also has an exponent? would i still write 0?

[MegaJesusfreaks]

Thank you so much helped a lot!!

[SVUfannyc]

Gracias! THANK the LORD FOR UR TEACHING SKILLS CUZ MY TCHR JUST BLABBERS AWAY....BLAHBLAH & DONT SHOW ME ANYTHING!

[danrbiv]

Thank you very helpful

[YangChunLee]

VERY HELPFUL~ THANKYOU SO MUUCH.

[1124missy]

THANK YOU SO MUCH.!!!!!!

[peaceplease]

I love you man.

[spongebobp11]

How would you rewrite the original fraction if the remainder was a negative?

But very helpful thank you!

[guntokill]

gracias ya no me acordaba :)

[rizalmafia06]

how to add 0 ? i mean where all the 0's came from? how will i know if im going to put them o my gosh, im dying now

[patrickJMT]

@rizalmafia06 i have no idea what you are trying to say

[patrickJMT]

@rizalmafia06 i have no idea what you are trying to say

[Champerbutt]

@patrickJMT i think they are trying to say. where did the 0 come from? when u took 0x^3 and brought down the zero. without seeing a previous video it was a bit confusing at first but after i saw ur long division video it made sense.

[Mintonetteable]

@rizalmafia06 every 0 that appears is placed because there arent x^3 nor x in the original....... x^4 =1, x^3=0, x^2=1, x=0..... think in descendant order;

[TheAniKinji]

@rizalmafia06 There are zeros because they skipped x^3 and x

[kangkimon]

@rizalmafia06 x^4 is equal to 1 x^3 is equal to zero. x^2 is equal to -1 and x is equal to 0

[xokatkat]

@rizalmafia06 since there are no values for x^3 or x, he puts zero in their place

[CarlosEnrique408]

@rizalmafia06 if its like x^4 + x^2 + x you put the zeroes where the missing x to the wwhatever powers would be. Since you dont have X^3 or a constant(the number by itself with no x) you put zeroes there. so it would be 1 + (no x^3 = 0) 0 + 1 + 0 (since there is no number after the last x with no power(^)). thats when you put the zeroes. @patrickjmt am i right?

[kimcaymo]

this will help me in my exams thank you so much.

[RidinMusicLines]

Mmmmm. The only issue I have (I still love this video) is that you do not simply take the opposite sign. You take the root.

So x + 3

x + 3 = 0

x = -3

My point is it can be more advanced than that and be difficult at a greater level.

[michaels6speed]

@multiblade77 you have to have consecutive descending exponents, if you skip a power just add a 0x^ like he did...or to fill in any missing Xpower.

[629shashi]

Cool vid, it's very effective. You're a genius dude. Thanks to you, no one can call me a noob on math now

[LhoneStar]

a non boring teacher on youtube yey! :D

[lpperalta1]

what is the use of knowing the value of P(x) when x = -3? (in this case) :D

[kohunterrr]

THANK YOU!

[Kenthis15]

Nice vid! I'm also left handed =)

[HxenGx]

thanks thanks thanks!! help in my math olympiad training!! (:

[livetoriga]

I can't believe that you would go through the trouble of making these incredibly comprehensive videos in your free time. You're a saint (Patrick)!

[DerrickDmx]

Great work indeed.

[amiful]

You have helped me so much! My math book is horrific at explaining things so your videos always help me get it. Thanks :)

[EbonfrothCovers]

in F(x), i could plug in any number, or it has to be the number that makes the divisor zero?

[DERmrVIKTOR]

the one person who disliked this was probably my sadistic math teacher.

[aquaristic]

Why would the result not be the same if it were a +3 in the f(-3) step at the end?

[4purs]

what do you do if it's divided by a different variable?

[Iamorton]

@ patrickJMT what if you have 6x^2 + 7x + 9 divided by 2x + 1 ,

then how would u do that?

[czam425]

@Iamorton you would divide each term by the coefficient of the number you are dividing by..(2x)

if i didnt explain it well there is a comment above he answered that should explain it

[HxenGx]

@Iamorton: i am a newbie and probably this might work...

divide 6x^2 + 7x +9 by 2 first, which u will get 3x^2 + 3.5x +4.5 divided by x +0.5. Then solve accordingly using synthetic division, a bit tedious than usual though

[toolbass24]

Thank u

[Iamorton]

GOD BLESS YOU!!!!!!!!!!!!!!!!!!!!!

[BoulderGirl1059]

First of all this is an extremely helpful video, so thank you for posting. I just have one question, what would you do if the x in the denominator has a coefficient?

[patrickJMT]

@BoulderGirl1059 you can divide each term by that coefficient 

[mayrafuerte123]

Can you use synthetic division for this? 6x^3+5x^2-8x+4/2x-1...I get confused when theres a number in front of the divisor

[jono1478]

This is a WAY better way then my math teacher was trying to teach it!

[patrickJMT]

@jono1478 not sure what your teacher was showing, but ultimately long division is what is most useful.

[dovegirl17]

Thank you for clarifying this for me :)

[BritRock93]

What happens when you get 0 as the remainder?? Is the ending result simply zero??

[patrickJMT]

@BritRock93 it means there is simply no remainder (so thatmeans you have found a factor)

[DaveyHiles]

Honestly, who would dislike this video?

[scout6686]

So can you only do synthetic division when the divisor is a monomial? or will it work with any polynomial divisor with a constant????

[CCprod422]

You have saved me :) Thank you so much, really.

[ohpeterrr]

thank you sooo much!:)

[z3ro146]

thank you so much for this instruction it saved me i have a quiz tomarrow and this video cleared the clouds in my confusion

[chaoshart]

wat if the divisor is 3x - 2 ? do i have to change it to fraction?if it does how do u solve it with a fraction?. pls do a video :(

[kochesstriker9]

i take algebra 2 in 8th grade and this helps out alot

[LovelyMissJessica]

what if the leading coefficiant is negative???

[patrickJMT]

@LovelyMissJessica the leading coefficient of what

[LovelyMissJessica]

@patrickJMT for example in this problem the x^4 , if that was negative , do you have to change it to positive , or is its okey to leave it negative

[foreverone23hill]

@LovelyMissJessica Then it remains negative. =))

[TheWhole9Yards1001]

smart irishman :)

[USNAVYIT]

Excellent followup to your first video. Clarified and answered all the questions I had from the first video.

[xxmtbxtremexx]

Don't you just love math!? >.> thank you for making it a bit easier Patrick.

[patrickJMT]

@xxmtbxtremexx u r welcome : )

[420BurnaBlunt]

whoever disliked this video is fwustwated

[420BurnaBlunt]

Keep it up brother, society and all of humanity needs people with skills like yours

[yeshimom]

thank u.... i understand everything now

[Eremenatar]

my math teacher explain all this within an hour. YOU!!! explained all this less than 5 mins WOW!!!!

[McBirdec]

so when you evaluate the function, you only plug it into the numerator? f(-3) would make the denominator zero but what if you did f(10)?

[josh1212121]

i love you

[dandadoom]

Thanks for the help!

[Summery05]

YOUR SO AWESOME I DO UNDERSTAND EVERYTHING FOR JUST 4 MIN BUT MY TEACHER TOOK HALF HOUR FOR THAT AND I DIDN'T CATCH ANYTHING!

[MsPepsiBlue]

How did the answer became x^3 even though the given term is in the power of 4?

[amiz00]

dude thank u sooooo much i rly wish u were my algebra teacher then i know i wouldnt fail :D

[7Blackberry]

how about if the x+3 will become 2x+3..what i am going to do with the 2??

[patrickJMT]

@7Blackberry multiply the numerator and denominator by 1/2

[dutymanmaster2]

where is the x^3 term? :S

[guitarnoobie07]

tada! :D

[KMoney4680]

PatrickJMT you have saved my life. I have a final tomorrow and I did not understand this at all untill i watched this video. Thank you so much.

If you're not already a teacher, you should definitly become one

[gogobobo1092]

thankz

[Jay2Sexy973]

so in synthetic division you have X, X squared, and X to the third. cause i notice how you put a zero when you didnt have an x term or a x to the square?? that's the only thing that confused me at 0:25, meaning the time on your video.

[disneystar26]

That you SOOOO much ... This REALYYYY helped ... <3

[pxbone]

thank you this is saving my 536 grades :)

[HeartSignSymbol]

Thank you you're very helpful! :]

[toopercentmlk]

Thank you, I missed lecture on this part of the chapter and you have helped out since I hate books ;)

[nofear9081]

Thanks for the help. Gave me a better understanding for my quiz that I have tomorrow. (5 Stars!)

[deadlybballer]

thank you sooo much for this video....i missed the last 2 days of school and this is all we learned in class and i missed it all.....soo u made 2 hours of homework into a good 15 minutes....thank you!

[arncko]

its only four mins!

[Kursk08]

Great video. I'm terrible at math. I always wondered where those extra zeroes came from.

[VolatilisUnus]

This was really helpful!

I haven't done this for a couple years and found my notes to be entirely useless; thanks for the vid.

[tomprman]

where the zero come from? help

[geewhizitsashley]

Again, great video. You're extremely helpful :)

[18PaulWall18]

Your Videos are very helpful!

I would have never figured it out without you

becuz i missed school when they did this =]

Thanks soo much

[sem420]

dude, thanks a lot . :)

[armor11acr]

Great video.... I couldn't figure out where the "extra" zeros were coming from... the second example made it very clear. Thanks!

[anking85]

hi, i was wondering how do you factor out a polynomial such as x^3-3x+2...i was told to use synthetic division but its not divided by anything...?? thanks!

[belovedsmiile]

you help soo much!!!

my alg teacher couldn't teach at all!

he just blabs on how rich he used to be

and how many cars and boats he owns....

LOL...thanks again (:

[RECO23DERTO33]

i wishh u were myyy teacher!! great help i have a test tomorrow and u juss made my life easier :)

[digichatte]

These are really great videos. I missed the lecture for my Precalc class on this stuff but here I am, ten minutes later, with a pretty good understanding of the concept.

Thank you for putting these on youtube!!!

[SawaLove]

This is sooo good... My math teacher explained this along with long division for an hour and I didn't catch anything. 5 minutes of this and little googling on the internet and I got them both on 10 minutes! You're great and I wish I had your brain... if not then you as my teacher xD

[Tim3Consum3r]

were d'you get 0x^3 ? 0:25

[fraser182]

You have to look at the coefficients, including the coefficients of the powers that dont exist. Eg. there is no x cubed hence coefficient is 0.

[ms47mysterious]

you really are a life saver.. or i shud say grade saver:)... thnx

[rayan641]

tY so much!!!!! dude you're the best i wish you are my teacher!!!

[Mahdensia11]

wow.. ur amazing at teaching. That only took me 10 minutes to learn 2 classes worth. I almost deify you

[Brandonlcosta]

So the whole goal of synthetic division is to get rid of the (x-#) on the bottom of the fraction?

[patrickJMT]

well yes, it simplifies..

just like if you simplify 10/2 you end up with 5 (that is, you get rid of the 2)

you are doing the exact same thing, only now you have a more complicated expression with a variable instead of just a number

[timy123123]

can someone please solve this probelm

(x^3-28x+48) divided by (x+4)

[UnWarierMage]

The only thing I'd say to make a little clearer for next time is that when you're synthetically dividing you use a monomial of the form x - k so x +3 becomes x - (-3) and we divide in synthetic division by k which is where the -3 comes from, and this is also the k which we plug back into the original function.

[Chalency]

Wee. We're studying Polynomial Function and our teacher gave this, i have no idea and my classmate suggested me to search about Synthetic Division, i think i have the answer for our assignment, thanks!

[patrickJMT]

you are welcome : )

[IkonPhenom]

wat if the given is x^7-128 / x-2 ......?

[UnWarierMage]

then your k would be 2 (the number we divide by in the synthetic division)

[r1dePrkCty]

How do you divide by a number like 2x-3??

[UnWarierMage]

You can't. It has to be of the form X - K... so I think that you could divide through by 2 and get x - 3/2 and use 3/2 in the synthetic division. (I THINK)...

[patrickJMT]

exactly correct!

[Poetrygurl54]

yo..u are a life saver OMG i thought i was gonna drown until you threw me a life jacket.

[patrickJMT]

now we need to build you a boat! : )

[merino1902]

i wish teacher were like this guy... life will be so much easier

[patrickJMT]

i am apparently a tough teacher : )

probably best that i only make math vids for you : )

[AkaiAllan]

what if the dividend (top) is larger number than the divisor (bottom number)?

[genegene009]

Thank you so much man! I just realized that it's just as easy as 1-2-3. Hahah! Thaaanks! :)

[msgeminigal]

Great info!

[bike27]

Thank GOD!! I love you man LOL xD helping me alot... how about trinomial??

[k00lkid333]

hey were doing this in class but we have to find the factor (in your video it was x+3,) how do i find out the factor. THANKS

[djsupersanty]

gracias baron ...le verdad you make so easy ojala y los maestros ensenaran asi ...thank u ...it help me a lot with my test ..

[song32290]

thank you

you make it so easy :< ur so much better than my math teacher.

T-T thanks again

[pantherNJOH]

omg! u saved my math-life THANKS=)

[hellokitysuicideclub]

these are fantastic

teachers today pretty much suck.

these videos teach me more than i learn in class, and i actually remember these.

fan-freakin-tastic <3

[arad21]

where did you learn all if this? my teacher is terrible, and you're a genius. Thanks for easing my Algebra pain.

[patrickJMT]

happy to help : )

[goleangirl]

tank you sooooo muuuch

[shortymatisse]

can you make a vid on log rthmics or watever its called

[mynamesnotbill]

How would you divide by a trinomial?

[rockerduff1231]

why is there 0x^3

[patrickJMT]

that is such a simple question as to confuse me... could you clarify what you mean?

[jetsandmets93]

I have Midterms tommorow ... you just saved me ... your awesome

[Qwerty48121]

thx man u r the best

[locked14]

So on a graph, the remainder would be the X coordinate and the given thing on the bottom... in this case x + 3 which is turned in to -3 is the y coordinate.., rite

[nicole951432]

thank you so much!!

[Tort3x]

yo man thanks i missed algebra ii the day we did this and our book has a sucky explaintion of this and i had no idea how it worke and you helped me out alot.

[fenixspirit367]

thnx i was always having trouble with this kind of divisions because i was getting ridiculously big numbers

[DeCooliePrincess]

THANK YOU! you added this today and i have a test on this tomorrow all of your videos help me so much with my advanced functions clas.. I absolutly think I'm horrid at math but your videos guide me and help me grasp these concepts with simplicity Im ever so greatful.