Graphing Higher-Degree Polynomials: The Leading Coefficient Test and Finding Zeros

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  • Опубликовано: 22 янв 2025

Комментарии • 135

  • @santialterman3066
    @santialterman3066 9 месяцев назад +14

    This is by far the best channel for explanations. I love how clear and visual you are, plus you answer the "whys" of math (to get the max we need calculus). Thank you

  • @kevindeng5781
    @kevindeng5781 5 лет назад +175

    I have a test tomorrow, thank you so much...

    • @muutrich
      @muutrich 4 года назад +5

      @Latifa Alawadhi this comment was made 9 months ago man, the guy passed the course already lmfao

    • @ciaraboone
      @ciaraboone 4 года назад +6

      mine is in an hour 😳

    • @ohmykeyss
      @ohmykeyss 4 года назад +4

      @@ciaraboone mine in 3 hours

    • @vapecat17yearsago85
      @vapecat17yearsago85 4 года назад +2

      Nah I ALREADY did the test.
      Teacher wants me to show work so I put this LMFAO

    • @Aaradhya9797
      @Aaradhya9797 3 года назад +3

      @@ciaraboone soo sad...🤣

  • @a.henderson22
    @a.henderson22 5 лет назад +30

    tthank you so much for making this video I really had no idea where to start with these problems

  • @justinac6465
    @justinac6465 4 года назад +10

    thank you so much! I am currently studying for a math cst test and this helped clear up some difficulties I had with higher order polynomials! thank you

  • @lastweek438
    @lastweek438 4 года назад +11

    thanks professor for making this video.it has further motivated me in loving the algebra

  • @mrdmajor
    @mrdmajor 4 года назад +31

    "If you're confused, watch this clip one more time"
    0:00
    "If you're confused, watch this clip one more time"
    0:00
    "If you're confused, watch this clip one more time"
    0:00
    "If you're confused, watch this clip one more time"
    0:00
    "If you're confused, watch this clip one more time"
    "What is up guuuuuys? I decided to become a RUclips 'content' creator!" 😂😭

  • @NickHope
    @NickHope 3 года назад +7

    The equation in the comprehension question should be x^4 + 5x^2 + 4 = y because x^4 + 5x^2 + 4 = 0 does not contain y, and is only used to find the x-intercepts; it is not the equation that we actually want to graph, which must contain y for the given answer.

  • @ninjakiwigames5418
    @ninjakiwigames5418 2 года назад +5

    Holy shit you explained this so perfectly my math teacher could never

  • @larssalembier7790
    @larssalembier7790 4 года назад +24

    There is a small error in the video: when he says that you can also use the y-intercept, he puts the y-intercept of the function somewhere around -2/3, but if you actually calculate the y-intercept by replacing all x'es with a 0, you can see that the y-intercept is (0, -3), so the drawing is incorrect, the extrema of the function are way more outspoken.

  • @mugiwaranoluffy4656
    @mugiwaranoluffy4656 2 года назад +3

    This guy is a big help ❤️

  • @al-farabinagashbayev5403
    @al-farabinagashbayev5403 6 лет назад +17

    Hi, nice video. I recommend you also to explain how to plot polynomials of multiple variables. It would be great)

  • @mohammedayman7864
    @mohammedayman7864 24 дня назад

    im from egypt and thats helped me so much ty sm :D

  • @foggedmirror3973
    @foggedmirror3973 5 лет назад +2

    How did you factor? I don't understand how you got the (x+3)(x+1)(x-1) at 3:43
    I know how to factor but this is confusing me a little. 😩

    • @eneu9069
      @eneu9069 5 лет назад +9

      Trinity Lugo x^3+3x^2-x-3
      Split in two pieces x^3+ 3x and -x-3
      Factor each x^2( x+3) and -1(x+3)
      Now combine (x^2-1)(x+3)
      Factor x^2-1
      X+1 x-1
      Now you have x+3 x-1 x+1

    • @foggedmirror3973
      @foggedmirror3973 5 лет назад +2

      @@eneu9069 alright, i can understand that a bit. Hopefully I can apply that to what I'm doing. 😓
      Thank you so much for the clarification.

    • @eneu9069
      @eneu9069 5 лет назад +3

      Trinity Lugo yea np we’re all here for help

    • @TheFirstNamelessOne
      @TheFirstNamelessOne 5 лет назад +1

      The method is factoring bu grouping.

    • @ict12-3a_aranetarannyb.2
      @ict12-3a_aranetarannyb.2 4 года назад

      @@eneu9069 8:30 in this one a same procedure of it? kinda confuse

  • @Joseph-xs2mo
    @Joseph-xs2mo 4 года назад +11

    6:49 RUclips’s red line is jumping out

  • @dhayn_gwyn
    @dhayn_gwyn 2 года назад +2

    thank you, god of math

  • @yukimaru4667
    @yukimaru4667 2 года назад +4

    I can't find the zeroes in the given question using the synthetic division. Can someone pls give a method to find the zeroes

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  2 года назад +1

      rational roots test, it's covered in my tutorial on synthetic division

    • @Gogogumball72
      @Gogogumball72 2 года назад +1

      You can also use the quadratic formula just rearrange it like this and you would be able to find x^2.
      (x^2)^2 - 5(x^2) + 4 = 0

    • @yukimaru4667
      @yukimaru4667 Год назад

      Thank you

  • @GmyB0202
    @GmyB0202 5 лет назад +9

    If all math teachers were like him or has his attitude I think many students wont need to watch this type of videos.

  • @rajeshbeniwalbeniwal6001
    @rajeshbeniwalbeniwal6001 4 года назад

    Finally......., I got it ....., Thanks a lot sir😍😍

  • @eyosuga3809
    @eyosuga3809 5 лет назад +8

    this tutorial is Damn good I think im' get at least check in this part of the quiz tomorrow

  • @johnvaldez6722
    @johnvaldez6722 3 года назад

    I don't mean to be pedantic here, but if you graph the equation shown at 8:18, x^4 - 5x^2 + 4 = 0, you're going to end up with four vertical lines with x-intercepts at x={-2,-1,1,2}. It seems like what you are really asking your students to do is sketch the graph of f(x) = x^4 - 5x^2 +4.

  • @joshyanza6130
    @joshyanza6130 4 года назад +1

    Thank you very much professor

  • @user-zo3wy4we3t
    @user-zo3wy4we3t 5 лет назад +4

    Will you have cheat sheet pdfs that cover everything that can be used to be printed out or saved? Or do i just have to take notes on the video?

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  5 лет назад +7

      I’ve thought about doing PDFs but it’s a lot of work, I suggest just taking full screen screenshots to make your own little slides.

  • @wdekeizer
    @wdekeizer 2 года назад

    thank you this is exactly what i needed

  • @joy_takoyakie
    @joy_takoyakie 4 года назад +2

    this is way better than going to school💕
    I literally understand it😎
    thanks again 😄

  • @ninjakiwigames5418
    @ninjakiwigames5418 2 года назад +4

    Ofc Professor Dave has a video on every topic I need to study. (insert a blessing from the lord meme here)

  • @RussianDog735
    @RussianDog735 3 года назад

    Thank you very much, This is so helpful.

  • @g02balitakarylleleonec.34
    @g02balitakarylleleonec.34 4 года назад +1

    3:46 How did we get (x+3)(x+1)(x-1)=0?

  • @princessmaedesacula0820
    @princessmaedesacula0820 3 года назад

    I'm literally answering my module and I visit the link reference on our topic. Thank you so much for explaining. I had learned a lot. I can share this to my very late teacher who doesn't spend time discussing that is why I don't know anything without this video. HAHAAHAAHA

  • @Soumyadip_Pal
    @Soumyadip_Pal 7 лет назад +2

    Hi there, would you like to make a series about Elliptic Curve Cryptography (ECC) in future? I would love to learn from you.

  • @amandaneves435
    @amandaneves435 2 года назад

    Thank you, sir.

  • @felipeshannkarln.121
    @felipeshannkarln.121 4 года назад

    Very infotmative. Impressive. I'll be subscribing

  • @sangyunlee4523
    @sangyunlee4523 4 года назад

    YOU ARE THE BEST -from KICS

  • @markstephenbueno4314
    @markstephenbueno4314 4 года назад

    I have a test later. Thank you!

  • @EllaSullivan-w8h
    @EllaSullivan-w8h Год назад

    you just explained everything my math teacher failed to do in a semester lol. thanks

  • @gabriel9668
    @gabriel9668 5 лет назад +1

    Thank you!

  • @guidopierdomenico5108
    @guidopierdomenico5108 3 года назад +1

    i understood everything except for the factorization of the comprehension exercise, can someone explain it to me? plz?

  • @shubhamkukreja96
    @shubhamkukreja96 5 лет назад +1

    Thanks for clearing my concepts of this topic
    Very nice method of teaching

  • @gianfrancobruschetta2423
    @gianfrancobruschetta2423 2 года назад

    Hi, what's the solution of the factoring?
    thanks.

  • @relaxee5159
    @relaxee5159 6 лет назад +5

    thank you, I have an algebra II test tomorrow and you probably saved me a failing grade.

  • @victorzoma2749
    @victorzoma2749 4 года назад +1

    Great explanations
    But 😄😄 how did you study on your own to understand at such deeper level?!!😁😁😁(aka your study tricks)

  • @SephBustamante
    @SephBustamante 7 месяцев назад

    has to be y=4 specifically on x=0 on the comprehesion test or nah?
    and how do i get 4 do i just plug in 0 on the x

    • @SephBustamante
      @SephBustamante 7 месяцев назад

      like on the (x+1)(x-1)(x+2)(x-2) because if you plug 0 in you do get +4

  • @sina1436
    @sina1436 3 года назад

    i see 2 zero does it get multiplied and gives 4?

  • @sislol3685
    @sislol3685 4 года назад +1

    Can someone explain me the comprehension quiz

  • @badmosss_jaaat
    @badmosss_jaaat 9 месяцев назад

    thank u for that saved my time

  • @brillantesgmari
    @brillantesgmari 3 года назад

    Thank you, Math Jesus

  • @biancafaith7569
    @biancafaith7569 2 года назад

    I still don't get it. How would you know how high will the turning point be till it goes back down or up?

    • @lena_utkina
      @lena_utkina 2 года назад

      we're dont. thats bc it's just sketch

    • @shivanshuawasthi2485
      @shivanshuawasthi2485 2 года назад

      it's just a rough idea about the graph of polynomial

  • @buica2566
    @buica2566 4 года назад

    Superb.

  • @chotuu5400
    @chotuu5400 3 года назад

    Thanks sir

  • @amantadi
    @amantadi Год назад

    professor, can you help me please the how to compute the apparent weight of a 60kg student standing inside a lift while he accelerates 2m /s square down ward, at rest and 2m /s square up ward, Just its formula pease.

  • @funtime6225
    @funtime6225 3 года назад

    you can get the y values by plugging the x'es in the equation.

  • @lynevertayzon8638
    @lynevertayzon8638 4 года назад

    Thankyou!

  • @zorobabe6258
    @zorobabe6258 4 года назад

    Thankyou so muchhhh

  • @AldreineMAlpas
    @AldreineMAlpas Год назад

    Uh when i tried to make the zeros in the checking comprehension its (x + 1)(x + 4i)

  • @zavryonthegrind6329
    @zavryonthegrind6329 Год назад

    watching while taking the test

  • @ronycb7168
    @ronycb7168 Год назад

    I got my mistake made a mistake to consider the zeros to be even multiplicty thanks for the video

  • @mr.perfect648
    @mr.perfect648 4 месяца назад

    Love from india ❤❤

  • @bullfrag4290
    @bullfrag4290 3 года назад

    i didnt knew you explain math problems

  • @ignacioleikis1784
    @ignacioleikis1784 2 года назад

    Is it cheating if I use a graphing calculator?

    • @carultch
      @carultch 2 года назад

      Depends on who's asking you to produce a graph of the equation.

  • @allenlobrigas7154
    @allenlobrigas7154 Год назад

    I have a test later and im gonna clutch it

  • @shhidayeasmin6147
    @shhidayeasmin6147 5 лет назад +2

    Can you explain maxima and minima by using calculus

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  5 лет назад +3

      yes i have a tutorial on that! somewhere in the calculus section, has to do with second derivatives

  • @Senjuu14
    @Senjuu14 3 месяца назад

    Help me to pass the quiz pls

  • @Asian_Boii
    @Asian_Boii 10 месяцев назад +33

    Me writing this comment to come back and tell myself the grade I got

    • @xama5x.
      @xama5x. 7 месяцев назад +1

      How much u got?

    • @biggestloseroftheday2598
      @biggestloseroftheday2598 7 месяцев назад +1

      yeah how much did this guy get

    • @Asian_Boii
      @Asian_Boii 7 месяцев назад +26

      @@xama5x. Oh yeah i forgot about this lol, got a solid 85% and ended my class with an A: 89.53 grade average!

    • @xama5x.
      @xama5x. 7 месяцев назад +1

      @@Asian_Boii congratulations

    • @drizzlealdc
      @drizzlealdc 5 месяцев назад

      @@Asian_Boii What class?? Alg2?

  • @brenazelda224
    @brenazelda224 2 года назад +1

    Ty ^v^ again

  • @ayoubelghazi8918
    @ayoubelghazi8918 4 года назад

    can someone explain to me how he resolved the comprehension equation?
    nvm I got it

  • @tGoldenPhoenix
    @tGoldenPhoenix 3 года назад

    Done.

  • @kristoffer1085
    @kristoffer1085 4 года назад

    thank you math jesus

  • @mosyotark1748
    @mosyotark1748 Год назад

    oh no 4:54

  • @bahauddinchishte
    @bahauddinchishte 3 месяца назад

    GOD bless you!

  • @geatsquared
    @geatsquared 3 года назад +8

    Thanks Jesus

  • @samuelcrisolo6080
    @samuelcrisolo6080 3 года назад +1

    It doesn't make any sense to me. 😵. Even though, thank you for teaching.

  • @manjupatil4717
    @manjupatil4717 3 года назад

    Nice intro

  • @Krai1234
    @Krai1234 4 года назад +2

    Long hair
    Beard
    Helping people
    Jesus is that you?

  • @senzuicodm6901
    @senzuicodm6901 2 года назад +1

    thank you polynomial jesus

  • @ajprincessderek6229
    @ajprincessderek6229 4 года назад

    Lmao I'm watching to learn for the test and the example is the same on the test
    I was looking for an explanation but I got the answer lolololol

  • @jurisenpaiikun1042
    @jurisenpaiikun1042 4 года назад

    thanks math jesus

  • @nerinedesu
    @nerinedesu 4 года назад +1

    I'm so dumb, i still don't get it...

  • @mmooonnoor6502
    @mmooonnoor6502 2 года назад

    ياريت تتاكدوا من جواز حكم وضع الموسيقى او الاغاني ع مقاطعكم عشان تتجنبوا الوقوع بالاثم وشكرا لكم ربي يحفظكم

  • @NinosEndlessVlogs
    @NinosEndlessVlogs 5 лет назад

    what the fuck im failing tomorrow

  • @faithelias2798
    @faithelias2798 3 года назад

    God loves you and he wants to save everyone, but in order for him to do that, you need to repent and be baptized. Also share his gospel with everyone you come in to contact with and keep his commandments 🙏🏾😘

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  3 года назад +4

      This is a math tutorial, sweetie.

    • @Teiwaz111
      @Teiwaz111 2 года назад +2

      @@ProfessorDaveExplains Math loves you and wants to save everyone, but in order for math to do that, you need to revise and be educated. Also share this knowledge with everyone you come in to contact with and keep science alive 🙏🏾😘
      There, fixed it for you 👍

  • @kaileybump4298
    @kaileybump4298 10 месяцев назад

    I wish you were my professor lol

  • @darrenvinculado4293
    @darrenvinculado4293 4 года назад

    I can't understand a single thing

  • @ochna000
    @ochna000 4 года назад +1

    yaann yaannnnn

  • @AlessandroZir
    @AlessandroZir 2 года назад

    ❤️❤️🙏🙌

  • @Senjuu14
    @Senjuu14 3 месяца назад

    Love from pakistan grape

  • @lawrenceleones2326
    @lawrenceleones2326 3 года назад

    Math Jesus

  • @bigbootybraxyn9801
    @bigbootybraxyn9801 3 года назад

    😃

  • @tacoexpressSEEDEEholeeveryones
    @tacoexpressSEEDEEholeeveryones 3 года назад

    men should only wear short hair