How To Find the Zeros of The Function

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  • čas přidán 1. 09. 2011
  • 👉 Learn how to find all the zeros of a polynomial by grouping. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values of x for which the value of the polynomial is zero.
    To find the zeros of a polynomial by grouping, we first equate the polynomial to 0 and then use our knowledge of factoring by grouping to factor the polynomial. Next, we use the zero-product property to evaluate the factored polynomial and hence obtain the zeros of the polynomial.
    Recall that the zero-product property states that when the product of two or more terms is zero, then either of the term is equal to 0.
    👏SUBSCRIBE to my channel here: czcams.com/users/mrbrianm...
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    Organized Videos:
    ✅Zeros of a Polynomial by Factoring
    • Zeros of a Polynomial ...
    ✅Zeros and Multiplicity of Polynomials | Learn About
    • Zeros and Multiplicity...
    ✅How to Find all of the Zeros by Sum and Difference of Two Cubes
    • How to Find all of the...
    ✅How to Find all of the Zeros by Grouping
    • How to Find all of the...
    ✅How to Find all of the Zeros in Factored Form
    • How to Find all of the...
    ✅How to Find all of the Zeros by Factoring 5th Degree
    • How to Find all of the...
    ✅How to Find all of the Zeros by Difference of Two Squares
    • How to Find all of the...
    ✅How to Find all of the Zeros by Factoring 4th Degree
    • How to Find all of the...
    ✅How to Find all of the Zeros of a 3rd Degree Polynomial
    • How to Find all of the...
    ✅How to Find all of the Zeros Without Factoring
    • How to Find all of the...
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    👨‍👩‍👧‍👧 About Me: I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. Find more here: www.freemathvideos.com/about-me/
    #polynomials #brianmclogan

Komentáře • 721

  • @b1kdmnd
    @b1kdmnd Před 7 lety +1747

    When you have to teach class at 9, but assassinate a target at 10

    • @brianmclogan
      @brianmclogan  Před 7 lety +281

      huh?

    • @tommydaape3412
      @tommydaape3412 Před 7 lety +350

      Free Math Videos
      you sorta look like the guy from hitman

    • @henryaugust98
      @henryaugust98 Před 7 lety +49

      yeah don't you know that if you're bald you automatically look like every other bald person??? Just like if you have blonde hair you automatically look like every other blonde hair person of course duh

    • @Xfighter000
      @Xfighter000 Před 6 lety +74

      He is referencing that you like the main character from the video game "Hitman".

    • @Xfighter000
      @Xfighter000 Před 6 lety +17

      Thanks for the help with this video by the way.

  • @Dark_Lord_Pixel
    @Dark_Lord_Pixel Před 3 měsíci +57

    Its currently 2024 and im watching this for math

  • @bieber89430
    @bieber89430 Před 7 lety +626

    My math teacher is very rude and likes to speed his way through a lesson without letting the class ask questions. Thank you for helping me and uploading these videos. You're a life saver :)

    • @brianmclogan
      @brianmclogan  Před 7 lety +89

      happy to be there for you, you are very welcome!

    • @atharmoughalandhammad1966
      @atharmoughalandhammad1966 Před 5 lety +6

      i have the same thing but with my social studies teacher
      the dude knows nothing about what he is doing

    • @fefe1179
      @fefe1179 Před 2 lety +2

      Our teachers are indifferent 😭!!

  • @mattwynes1689
    @mattwynes1689 Před 4 lety +160

    8 years later and this dude saving me lol

  • @homiz96
    @homiz96 Před 8 lety +1189

    This is very helpful, my teacher this year is not good

    • @brianmclogan
      @brianmclogan  Před 8 lety +192

      +homiz96 sorry to hear about that, teaching and recording myself all year.

    • @MichaelMoldovan3
      @MichaelMoldovan3 Před 6 lety +1

      Same

    • @jeonmingo_o
      @jeonmingo_o Před 5 lety +22

      Same my teacher is just sooooo boastful and sooo annoying af🤙🏻

    • @grace_alyssa2167
      @grace_alyssa2167 Před 5 lety

      Sameee

    • @shaziach6078
      @shaziach6078 Před 5 lety +3

      Teqcher are always good but the difference is we r not ablr to get the point that what they r actually trying to make us understand

  • @braydenritter2273
    @braydenritter2273 Před 4 lety +7

    i’ve been trying to learn how to do this for 2 months, and then it took 3:05 minutes of this video for me to 100% understand it. Bless up for this dude

  • @calebpullen7552
    @calebpullen7552 Před 7 lety +193

    Dude, you're awesome. I wish I had you as my teacher!

  • @lakeofwindows9653
    @lakeofwindows9653 Před 6 lety +106

    I've been struggling with this concept and going into a mild panic attack due to having an exam on this in the morning. Really wish I found your videos a few weeks ago when I began studying for this exam, but better late than never I guess. Thank you so much!

    • @brianmclogan
      @brianmclogan  Před 6 lety +17

      you are very welcome! you will be okay. Keep working hard

  • @FancyPants208
    @FancyPants208 Před 9 lety +157

    Really saved me for my pre calc test lol. This video was a good refresher.

    • @brianmclogan
      @brianmclogan  Před 9 lety +17

      FancyPants208 awesome! happy to help you out

    • @lukeochoa3450
      @lukeochoa3450 Před 4 lety +5

      Hey, I’m u, but like 5 years later :D

    • @user-nk5us7jw1s
      @user-nk5us7jw1s Před 4 lety

      Luke Ochoa XD

    • @bellaklein8692
      @bellaklein8692 Před 3 lety +2

      woahhh u took calc in 2014???you're probably like 24 now :0 hope you're thriving

    • @applesaus395
      @applesaus395 Před 2 lety

      Now I want to see a life report

  • @Spook_1994
    @Spook_1994 Před 11 měsíci +12

    Over the years when I have been confused while studying math, I have always been able to find a solid explanation on this channel. Thank you for your hard work!

  • @brianmclogan
    @brianmclogan  Před 11 lety +16

    we introduce this in Algebra 1 but go much deeper in pre-calculus. Keep up the hard work

  • @bandawin18
    @bandawin18 Před 3 lety +1

    After all these years and every time I come back to this channel there's always something there to help me with whatever I need. Truly awesome

  • @brianmclogan
    @brianmclogan  Před 11 lety +39

    thanks, your comment had me cracking up this morning.

    • @zigfoe3292
      @zigfoe3292 Před 3 lety

      @Verena Faheem doesnt factor

    • @bellaklein8692
      @bellaklein8692 Před 3 lety +1

      @@zigfoe3292 i think thats a little late lmao

    • @zigfoe3292
      @zigfoe3292 Před 3 lety +2

      @@bellaklein8692 tbf he replied to a 8 year old comment while mine was just a few months behind, regardless it's never too late to learn :D

    • @bellaklein8692
      @bellaklein8692 Před 3 lety

      @@zigfoe3292 tru that

  • @seamusmoran4776
    @seamusmoran4776 Před rokem +4

    dude I cannot even begin to express how helpful these videos are, you're the sole reason I'm surviving pre calc

  • @chi3fsquanch124
    @chi3fsquanch124 Před 5 lety +73

    When u gotta teach class at 8 but got a meeting at the casting couch at 9

    • @pixoljef7830
      @pixoljef7830 Před 4 lety +41

      when u copy a comment at 8 and make it worse at 9

    • @dsnow7211
      @dsnow7211 Před 3 lety +1

      @@pixoljef7830 when you copy the copied comment out of sarcasm but it makes even less sense

    • @pixoljef7830
      @pixoljef7830 Před 3 lety +3

      @@dsnow7211 lmao I remember that joke I made years ago. Really brings tears to my eyes. 🥲

  • @brianmclogan
    @brianmclogan  Před 11 lety +14

    Your right, the best way to overcome this is to practice. I know that is a cliche answer but the more you practice the more your confidence will grow

  • @ColeEasley
    @ColeEasley Před rokem +3

    been struggling with this all year, never truly understood it until I found this. Thank you so much!

  • @kassandramartinez-rodas9197

    I had a teacher that taught like you in high school, now that I am in college teachers just ask us questions and expect us to know it all without an explanation. Thank you!!!!

  • @brianmclogan
    @brianmclogan  Před 11 lety +10

    This is pre-calculus. Keep up the hard work!

  • @brianmclogan
    @brianmclogan  Před 11 lety +14

    don't worry I have examples of those types of problems too. When you have two (x-4)'s as your factors we can re write it from (x-4)(x-4) to (x-4)^2. Now our factor is raised to an even power. When we have a factor to any even power it is said to have even multiplicity. What does even multiplicity mean? It means that the graph will touch and rebound at x=4 rather than cross at x=4. However x=4 is still a zero of the polynomial. Did that explanation help?

  • @sarge7526
    @sarge7526 Před 7 lety

    I am loving your videos! Thank you for explaining and even giving students a chance to ask questions on how you came about with your answer

  • @abdullahdandal1406
    @abdullahdandal1406 Před rokem +2

    I swear thank you so much man. I have final exam after tomorrow, and this is the only thing I couldn’t understand, but now thanks to you I understand. Again I say thank you so much.

  • @DeliveryGuy23
    @DeliveryGuy23 Před 3 lety +1

    I know you already got a million of these types of comments, but thank you for helping me understand math just a little bit more. I haven't had a real math teacher since 7th grade (multiple first year teachers got fired because the class refused to listen, and bullied the teachers, then student's parents would be the "substitute" for the rest of the year, but would just give us the answers). Now I'm in college taking a math course and my professor speeds through the problems. So fast that I cannot write everything down while trying to understand what is happening within the problem. She insists that everything is "easy" and it's the "simplest" thing to do, but I struggle hard for hours trying to do my homework, and when I watch your videos I finally go, "ooooooohhh!".

  • @brianmclogan
    @brianmclogan  Před 11 lety +2

    you are very welcome! happy to help

  • @joalmeria891
    @joalmeria891 Před 6 lety +31

    I wish I had this guy as my teacher

  • @arcos8917
    @arcos8917 Před 5 lety +9

    @3:57 is me contemplating my life this semester lol Thank you for your help!

  • @OluwafunmiO
    @OluwafunmiO Před 6 lety +5

    Oh my goodness! This tutorial was awesome! I'd been struggling with polynomials for hours but Brian was so easy to understand. Solved a few math problems in a couple minutes! Thanks so much

  • @emilyy9008
    @emilyy9008 Před 4 lety

    I love how you actually explain what your doing as ur doing it.

  • @Jessica-hl4mo
    @Jessica-hl4mo Před 5 lety

    I searched on youtube to explain the same question the person in your video asked about, and that was the clearest answer ever!!! Thank you

  • @Its_A_Meag
    @Its_A_Meag Před 7 lety

    I have been looking for hours to find a way to explain this for upcoming exams, you do it in such a way which makes it so much easier to understand! Also due to you doing it in a classroom with students it makes it feel as though they are asking for us! Great work your my hero at the moment!

    • @brianmclogan
      @brianmclogan  Před 7 lety +2

      you are very welcome! Happy to be there for you

  • @sakaue
    @sakaue Před 4 měsíci +1

    this is the best channel i have ever found for my gpa. thank you so much.

  • @brianmclogan
    @brianmclogan  Před 10 lety +4

    perfect! happy to help

  • @evilskater9652
    @evilskater9652 Před 3 lety

    You are literally the only teacher I understand math from!!! You are helping me so much with my pre calc class

  • @Xxsportfreek17
    @Xxsportfreek17 Před 8 lety +2

    Thanks for all of your help! I appreciate it. You're really helping math students everywhere keep up the great work you're the man.

  • @JustJayYoutube
    @JustJayYoutube Před 5 lety +4

    Thx for this so much! Your better than my teacher so I always find myself to come here!👍🏼

  • @demolish000000
    @demolish000000 Před 8 lety +10

    A true visionary. Thank you!

    • @brianmclogan
      @brianmclogan  Před 8 lety +4

      +demolish000000 you are very welcome! happy to help

  • @savitmalhotra3717
    @savitmalhotra3717 Před 2 lety +1

    Its currently 2:17 AM on August 27th, 2021. It has been almost 10 years since this video came out and he is the reason why I will finally get to sleep tonight!

  • @brianmclogan
    @brianmclogan  Před 10 lety

    you are welcome, happy to help!

  • @angelacobrinlandis
    @angelacobrinlandis Před 8 lety

    Thanks so much! I've been watching your channel for a while and it never fails to impress me! I always need help in math and this is my GO-TO place! Thanks for doing what you do!

    • @brianmclogan
      @brianmclogan  Před 8 lety

      +angelacobrinlandis great to hear, so happy I am able to help you out!

  • @brianmclogan
    @brianmclogan  Před 11 lety +2

    might be hard but I am very happy that you are learning

  • @lizsanchez5699
    @lizsanchez5699 Před 3 lety

    I've been looking for this kind of problem and I finally found a useful video! Thank you so much!

  • @bronco7087
    @bronco7087 Před 4 lety

    Duuuuuude you’re an awesome teacher! My teacher does things way too fast and my friend who has a different teacher for algebra 2 tried to explain this to me but I was still confused. You’re a lifesaver!!!

  • @charlieg3674
    @charlieg3674 Před 3 lety +1

    Thank you so much! With virtual school this year it's been really challenging to have proper instruction

  • @ashleynichole5692
    @ashleynichole5692 Před 5 lety +2

    With this explanation about factoring by grouping I finally understand what's going on. Literally aloud "Ooohhh!"

  • @soysawce1908
    @soysawce1908 Před 8 lety

    I want to thank you so much! I had no idea how to find zeros because my teacher doesn't teach well and she's only been teaching for one year. She tries to dodge every question we have and doesn't answer it fully when she receives one. But now that I found you, I feel ready for my midterms now! Thank you!

    • @brianmclogan
      @brianmclogan  Před 8 lety

      +soy sawce great to hear. Keep up the hard work and let me know if there is anything else I can do for you to assist you.

  • @FlowerRFabulous
    @FlowerRFabulous Před 5 lety +5

    holy moly, please come teach me calculus!!!
    i like your tempo!

  • @heerbhavsar
    @heerbhavsar Před 3 lety

    I am having my exams rn and this is a really great way for me to review for everything i learned in class. Thank you!

  • @perry0987654321
    @perry0987654321 Před 3 lety +1

    you are my go to right now during covid, just need this kind of teaching all the time lmao

  • @lillypad202
    @lillypad202 Před 4 lety

    I have a whole unit of math hw due today at midnight n all of his videos are saving me rn

  • @azhannayeem4030
    @azhannayeem4030 Před 5 lety

    Thanks a lot! You are an amazing maths teacher!

  • @reish_krispies3138
    @reish_krispies3138 Před 7 měsíci

    12 years later and I'm still learning from this legend

  • @jameswhyte1340
    @jameswhyte1340 Před 9 lety +8

    Great lesson and thorough explanation.

    • @brianmclogan
      @brianmclogan  Před 9 lety

      James Whyte thank you! happy to be able to help

    • @jameswhyte1340
      @jameswhyte1340 Před 9 lety

      No, thank you! I've been watching your videos for a few years now without them I don't know if I would have passed! Thank you for your clarity. Keep up the great work!

    • @brianmclogan
      @brianmclogan  Před 9 lety

      James Whyte will do!

  • @amiteshbehera6442
    @amiteshbehera6442 Před 4 lety +1

    In India cbse our maths is way tougher than this.... Specially class 11 and 12 syllabus for IIT JEE..... Very complex problems in Physics Chemistry and Maths... But very well explained sir thanks to u keep it up ur really a nice teacher

  • @liz813solis1
    @liz813solis1 Před 11 lety

    Yur videos are really helpful! and im taking college algebra and with yur videos I seem to understand it better :)

  • @Tapport
    @Tapport Před rokem

    In case anybody isn’t understanding the part the student asked about, here’s how to understand exactly what factoring out is doing in this equation:
    x^2 (x-4) - 9 (x- 4) gets rewritten as (x - 4) (x^2 - 9) because when you distribute (x - 4) you get [(x - 4) * x^2] - [9 * (x - 4)] which is x^2 (x - 4) -9 (x - 4).
    What’s happening when you factor out is you’re doing the reverse of distribution. It gets confusing because up until this point in math, you’re most practiced in doing it one way instead of the other, but the process is doing the exact same thing just in reverse.

  • @sarahmarzugi8516
    @sarahmarzugi8516 Před 2 lety

    10 years later and he’s still so helpful

  • @joelwon3451
    @joelwon3451 Před 5 lety +5

    Helped me during the algebra test

  • @ibeatkids3803
    @ibeatkids3803 Před 10 měsíci

    As an indian, I wish you were my teacher. Whenever I ask my teachers doubts, they just get mad for no reason. Good work with the explaining

  • @brianmclogan
    @brianmclogan  Před 11 lety +1

    Most people need to see something a couple of times before it can sink in. CZcams is excellent for that

  • @timothyrushing7505
    @timothyrushing7505 Před 5 lety

    Wish I had you as a teacher. I actually considered dropping out of college because I had such a terrible teacher but thought it was just me being too dumb to understand math. You're way better.

  • @brianmclogan
    @brianmclogan  Před 11 lety +3

    You have to either use factoring, quadratic formula or use your calculator to find the zeros

  • @juliadockendorf8047
    @juliadockendorf8047 Před 10 lety

    This helped so much!! My pre calc teacher doesn't teach us anything and this problem was right out of our textbook

  • @patriciaacosta2664
    @patriciaacosta2664 Před 5 lety +1

    Thank you so much for these awesome videos!!!

  • @maryalissa112
    @maryalissa112 Před 4 lety +2

    I am online schooled so I love watching these because it reminds me of being back in actual school LOL and they are more helpful then my online lessons so

  • @fabianfelix513
    @fabianfelix513 Před 4 lety

    great teacher, super reliable source

  • @lkat718
    @lkat718 Před 6 lety +1

    Thank you so much! An oldie but a goldie! My teacher hasn't explained this in a semester as well as you did in 2 minutes :)

  • @wolf2623
    @wolf2623 Před 5 měsíci

    Thank you. Very easy to understand.

  • @sensitivemeat284
    @sensitivemeat284 Před 3 lety

    Your videos are perfect for the 2021 lockdown my teacher isn’t good at explaining math and if we don’t understand its to bad so sad. So your videos have been teaching me more then my teacher thank you

  • @CodedGames
    @CodedGames Před 11 lety

    I don't know why but I learn a lot better when its on CZcams. I thought this was really hard in class but now it makes a lot more sense.

  • @rinati75
    @rinati75 Před 4 lety +7

    Damn girl had to cough right when the question and answer were being discussed...hold your cough! 🤣

  • @babsaibuckleup4380
    @babsaibuckleup4380 Před 2 měsíci +1

    12 years later hes still saving lives 😭😭

  • @ezralai415
    @ezralai415 Před 6 lety

    Thanks for the refresher! Now i've gone through everything for the algebra 1 regents in 2 days!

    • @brianmclogan
      @brianmclogan  Před 6 lety

      awesome! happy to be able to help you out!

  • @davidwoodywoodpecker1967

    THANK YOU SIRRRR!!!! THIS HELP ME A LOT DURING MY LECTURE CLASS. NEVER MISS YOUR VIDS SIR!!..THANKS AGAIN.

  • @noemibertuola7223
    @noemibertuola7223 Před 5 lety

    i always enjoy and understand clearly your videos, thank you for making them, my teacher is not helping at all and i don't know what do to to pass the course, thank you!

  • @aaronkintzer3943
    @aaronkintzer3943 Před 3 lety

    9 years later...and youre still helping people :D

  • @angelskisses43
    @angelskisses43 Před 11 lety

    Lol, I like your pace. Boom boom boom. This was really helpful, thank you so much!!

  • @iCraft54Games
    @iCraft54Games Před 5 lety

    Forgot to factor and find the zeroes. This helped a lot. Thank you!!!

  • @GGz613
    @GGz613 Před 8 lety

    Thank you ,thank you so much ! You have no idea how much this small video just helped me.

    • @brianmclogan
      @brianmclogan  Před 8 lety

      +hira muhammad happy to be able to assist you!

  • @brianmclogan
    @brianmclogan  Před 10 lety

    you are very welcome!

  • @Mushy_guy
    @Mushy_guy Před 7 měsíci

    thank you ive been over thinking this all day trying to figure out if i was doing it right or not W vid

  • @rosiewoodland23
    @rosiewoodland23 Před rokem

    Thank you, I love your videos. They help a lot!

  • @ayanosakura2100
    @ayanosakura2100 Před 5 lety

    This channel needs more subs, my teacher told us this year in preparation for college he would just help us if we had any questions and that we had to learn everything ourselves. I mean I would hope they still teach students in college??? I mean what's the point of college if you don't get taught? What am I spending my money on then? Then again I wouldn't be here if it wasn't for all the worksheets and lack of guidance

  • @Iman-vm8hj
    @Iman-vm8hj Před 11 měsíci +1

    Fun fact: sir, you have single handedly just saved me 👍 and I can't thank you enough!

  • @christinalogan3755
    @christinalogan3755 Před 6 lety

    Thank you!! I was having trouble with how to factor polynomials with 4 or more monomials. Your explanation was very clear and concise and I found it extremely helpful. Also, In the video when the girl asks about "where the other x-4 went" I wonder if it would have helped her by doing the reverse math by "distributing" the x-4 four back in so, that she could see that you are actually multiplying it by all of the pieces and therefor you haven't actually lost an x-4. I needed that when I too, didn't understand "where the other went" haha Thanks again.

    • @brianmclogan
      @brianmclogan  Před 6 lety

      you are very welcome! yes I agree, that is often a hard part of factoring by grouping, would have been a good opportunity to address that there

  • @daedgoco
    @daedgoco Před 9 lety +4

    THANK YOU! I was freaking out, my final is tomorrow and we only saw this last yesterday.

    • @brianmclogan
      @brianmclogan  Před 8 lety +1

      Daniel Gómez perfect! happy to be able to help you out!

  • @ihsakake
    @ihsakake Před 6 měsíci

    Couldn't understand how to find zeroes for the life of me. This was super helpful, I'm glad I found this, even though I'm 12 years late lol.

  • @STOB3N
    @STOB3N Před 7 lety

    You have no idea how much you helped. My professor knows how to do the problems, however he can't explain to the class very well.

  • @patrickobrien9125
    @patrickobrien9125 Před 11 lety

    Thank you so much! This really helped me!

  • @crazyisthenewawesome9369
    @crazyisthenewawesome9369 Před 5 lety +1

    dude thank you so much! LIKE THANK YOU!

  • @jeremiahallentennis77
    @jeremiahallentennis77 Před 3 lety +1

    test in an hour... this was a life saver

  • @leospiegel1311
    @leospiegel1311 Před 4 lety

    wow, great video! I 100% needed this!

  • @user-ob1sl8xh1u
    @user-ob1sl8xh1u Před 8 měsíci

    my professor teaches this very complicated, the way you teach it makes sense to me. I got the right answer just did it differently.

  • @geoninja8971
    @geoninja8971 Před 7 lety

    Great video. I hadn't thought of that way - I just plugged through a quick graph to get an idea of where zero's would be, then found x=4, then long division had the other term. Much more tedious....

  • @nnennaabigail1617
    @nnennaabigail1617 Před 6 měsíci

    Very clear solutions 👍👍

  • @kiaritheyoungin1928
    @kiaritheyoungin1928 Před rokem +1

    I think i need to start watching you Fr cause my teacher doesn’t explain how she got things very well but now watching this I understand and this is way easier than her method thank you!!!

  • @vespineragons7568
    @vespineragons7568 Před 3 lety

    This video helped me so much! Thanks!

  • @missmousers
    @missmousers Před 3 lety

    Do you have a video for the other direction? I’m trying to find the polynomial given the zeros of -2,1 and 4 with a degree of 4.

  • @barbecue_chickn1570
    @barbecue_chickn1570 Před 8 lety

    Thank you so much. Makes much more sense now !

  • @patriotguy12
    @patriotguy12 Před 7 lety +1

    found this very helpful thank you

  • @Chiko-sc1gz
    @Chiko-sc1gz Před 5 lety +1

    Thanks its was very helpful