Finding The Zeros of Fourth Degree Polynomial

👉 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: www.youtube.co...
❤️Support my channel by becoming a member: / @brianmclogan
🙋‍♂️Have questions? Ask here: forms.gle/dfR9...
🎉Follow the Community: / mrbrianmclogan
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...
🗂️ Organized playlists by classes here: / mrbrianmclogan
🌐 My Website - www.freemathvid...
🎯Survive Math Class Checklist: Ten Steps to a Better Year: www.brianmclog...
Connect with me:
⚡️Facebook - / freemathvideos
⚡️Instagram - / brianmclogan
⚡️Twitter - / mrbrianmclogan
⚡️Linkedin - / brian-mclogan-16b43623
👨‍🏫 Current Courses on Udemy: www.udemy.com/...
👨‍👩‍👧‍👧 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.freemathvi...
#polynomials #brianmclogan

[@brianmclogan]

glad I could help, its fun when those things finally start to make sense

[@iftikharshamsniloy8579]

Thanks a lot ,sir. I really appreciate your effort ! You helped me a lot. May Allah bless you.

[@liankhai6019]

LOL my math teacher is too lazy to teach so she told us to watch this video

[@brianmclogan]

here for you!

[@mohammadshahade8753]

what if she saw your comment ?

[@darthsion3844]

@@mohammadshahade8753 maybe it's not the real name? Lol

[@annhashi1768]

Lol

[@DennisBolanos]

LOL.

[@Bigschmitt25]

Thank you this helped a lot! I also love how you dont even edit out you calling out your student for not paying attention. I was laughing my ass off at that.

[@brianmclogan]

+Nick Meme you are welcome! yep it's the real deal, life in my classroom

[@brianmclogan]

I don't know why I said you couldn't factor by grouping for this problem. You certainly could. I think I was more concerned with showing how to solve using rational zeros

[@deedeeOWL]

👍🏼 I like how the teacher have include all zeros (even the imaginaries) so students see the big picture, and think in terms of Complex: Real and Imaginaries

[@Riverbend1752]

I'm a sophomore in college, and the professor teaching my differential equations course linked this video in our study materials. Thanks for putting it out there. It had been so long since I took an algebra class that I had forgotten how to do this, but this was a really approachable way to relearn it.

[@DeadKingKnight]

I’m going through the same thing in differential equations as well 🤣🤣🤣

[@she8334]

Are we living the same life? a sophomore too, and I am here because of my differential equations course

[@souryour6598]

You learn this in collage, im learning it in year 9

[@Riverbend1752]

@@souryour6598 I hope you are also studying English. One does not study at collage; they study at college.

[@brianmclogan]

I appreciate your kind words

[@kelvin26k]

some of those kids had no idea how blessed they were to have a good professor

[@bksupply8186]

So lucky i found this channel

[@mt33205]

I'm taking engineering and watching this guys vids for finals, really shouldn't have skipped so many lectures...

[@asystoleD]

0:45 LMFAO

[@brianmclogan]

haha some things never change

[@aliris19]

I'm a parent struggling to explain "CC" math to my kid and wow do I appreciate your videos. Thank you!!!

[@brianmclogan]

+Sara Roos you are very welcome! happy my videos are helping!

[@khushibarnawal9271]

Sir your videos are easy to understand... I wish I could study with you in my school.

[@brianmclogan]

happy they help, visit them whenever you neeed

[@those.gamers.]

ah thank you, my math teacher expected us to do a packet with a question like this and didn’t teach it lol

[@anjugupta25]

Taefan!

[@1v1noscope37]

Was going crazy trying to figure out how to factor these, appreciate the help 💪

[@kmillz7414]

Brian, your videos continue to help me everyday. Thank you for doing what you do...and please continue to do so.

[@yzel36]

Your channel is a life saver thank goodness I found these videos

[@Starscrayper]

With your help, I'm able to cram for my college algebra test, and I am infinitely grateful for this.

[@brianmclogan]

happy to be able to assist you

[@brianmclogan]

When graphing this polynomial see that there are no real roots. Meaning their are no real zeros you can solve for(x-intercepts)

[@MPV2023]

Brian McLogan ...can u find me the roots for below eq'n... s^4+12s^3+91s^2+150s+50....???

[@Hahaalot]

Yo my nigha! Literally in college Algebra and used this video for my homework. Completely forgot parts because of spring break. U's the real MVP! Thanks my guy! :)

[@brianmclogan]

happy to help

[@Historyhappenshere]

Brian is saving my life right about now

[@seth-langendoen]

All he said was "factor by grouping" in the beginning and I could solve my question.

[@JLvatron]

Great explanation! And who are the fools at 0:42 disturbing class!!

[@ganeshnithiyananthan8487]

thanks for these videos really helped a lot for my exams

[@jerryfan8378]

At 8:46 shouldn't it be i*sqrt of 2? This way, when you put "i" in the equation, it will change sqrt of -2.

[@user-vm3lz6ve6g]

Yes, I noticed that too sqrt(-1) = i, therefore you are correct.

[@900q8]

tysm this helped a lot!

[@mammamia151]

Thank you so much for helping me with my math homework!

[@AbigiyaNega]

Can i ask what grade u teach it's very helpful

[@ansenliu]

Thank you so much, you're a good man, you deserve honor :)

[@FreeDomSy-nk9ue]

The trick you mentioned about the constant is just amazing

[@brianmclogan]

happy to help

[@ShivaPrasad-hm5lk]

superb excellent.......... I liked ur explanation continue

[@brianmclogan]

awesome!

[@boywonder_YT]

Tristen, you really gotta listen buddy.

[@marymccory8075]

Great!!!!! I should have came here for help a long time ago!!!!!

[@brianmclogan]

+Mary Mccory here all year long

[@darrelseibert420]

one hell of a video thanks for clearing up the whole if it isn't to at least the 2nd power it is a 0 thing. also i am glad to see a thorough explanation to your work. For example, my teacher never really elaborated with the remainders in synthetic division and I had no clue what it meant. Wish me luck on my quiz tomorrow.

[@brianmclogan]

Darrel Seibert Good Luck! keep up the hard work and let me know how you do

[@remytherat2175]

THIS SAVED ME THANK YOUUU

[@oskarlindelof9685]

I solved it using factoring, this is how I did: z^4-4=(z^2+2)(z^2-2) -z^3-2z=-z(z^2+2) z^4 -z^3-2z-4=(z^2+2)(z^2-2)-z(z^2+2)=(z^2+2)(z^2-2-z) z^2-z-2=0 or z^2+2=0. Using the quadratic formula you can then determine that the roots are -1, 2 and +/-sqrt(2)i.

[@brianmclogan]

you can do that too

[@devan7485]

take in these kids are like 30 years old now

[@shravanikharkar4687]

My teacher suggest me this channel To better understand 😊

[@legendneverdiegaminglndg4136]

Sir can you tell me who was the student ?

[@livfrazier6295]

Wow, this was explained so well. THANK YOU!

[@brianmclogan]

+Olivia Frazier you are very welcome!

[@BehindTheHunt9579]

Sir you are the best

[@gsbedi68]

Wow !! Thank you for the help sir!! You were amazing !!

[@jesuisravi]

Question: What do you call the course you are teaching here? Is it Algebra 2 or precalculus or what?

[@nonokay20]

You are a great teacher!!!!

[@monicamedina3838]

I Need Your Help !! You Are Very Good At Teaching !! Can you Help Me With This Problem !! Please x^5+7x^3-x^2+4x-21!! It's A Problem on My Homework and It Says to Determine The Number of Roots that Each Polynomial will have. I Don't Understand It !! Please Get Back To Me.

[@aadamrayanbinabu]

the polynomial x^5+ax^4+3x^3+bx^2+a where a and b are constant has a factor (x-2)^2 using the factor theorem and the result of part (i) otherwise find the value of a and b.

[@brianmclogan]

sorry I do not have time to work on extra problems for students as I receive multiple requests

[@huankoi3403]

i'm from vietnam and it's very simple here

[@rolandpoland5363]

Helped me pass too many Alg 2 tests

[@Yuniferpeace]

Thank you isn't enough!

[@bluekai3317]

this make me feel like im in actual class tho it's online class now bc of corona

[@annhashi1768]

Thank you sir it really helped me .

[@paulinjosepha2336]

Good Job Professor and thank you so much for this video. I have Mid-term of Math 34 differential equation on the Wednesday , i was struggle to understand this part . However your video give me 10 points already. Again, thank you so very much.

[@brianmclogan]

happy to be able to help you out!

[@gr8tmeg]

why in the beginging couldn't do you factor by grouping? you could group z^4 and z^3 together, and -2z and -4

[@lanyahunar2659]

What if you tried all number and not equal to 0 to factor it?? please answer

[@Jumong34]

Why is the q ±1?

[@sohamparekh]

Very helpful, thank you.

[@heystobit2608]

Sir, can we use another method other than factorization.

[@cadmiumbop]

so for that polynomial there is only 3 roots even though it is an x^4 polynomial? is it something to do with the fact that there is no x^2

[@thomasjones145]

Thank you, this helped me so much!

[@eunicedickson9526]

What if this method also doesn't work for me? I'm solving x^4 + 2x^2 - x - 3 = 0. Any help please?

[@dash15yearsago67]

6:17 wouldn't we have to use rational root theorem again?

[@ryanostertag3570]

bro we down bad asf rn

[@kushalchakrabarti240]

Sir.. big fan!

[@brianmclogan]

cheers! happy to help!

[@Jakomaniac1]

Bless your soul

[@jonathanjohnson7508]

What would you do if there were no rational zeroes for a polynomial to the fourth degree? I know it'd require imaginary numbers, but I don't know how to factor it and get a+bi

[@RzVids]

You'd divide P/q and use that answer for synthetic division? That's if 1 and -1 doesn't work. So (in the same problem), you could try 4 and -4? 2 and -2? Does the Rational Zero test always work? What if you couldn't factor by grouping and if you didn't have another factor?

[@brianmclogan]

best bet is to graph the polynomial to find the zeros and go from there, however if you are not allowed a graphing calculator then yes Rational zero test will give you every zero that is rational. Only problem is you don't know which one till you test them

[@danpost5651]

In nine years, did no one catch your error that sqrt(-2) is not +-sqrt(2i), but +-sqrt(2)*i ? It appeared to me that (the wrong one) is what you wrote on the board twice.

[@ipihu]

Thanks you helped a lot I want tutions from you if you can plz

[@STYLEDBYSAMLAW]

ur a god dude thank you so much

[@splabicado6510]

my teacher always told us that the degree of the polynomial is the amount of solutions it has, but here you only got 3 solutions for a degree 4 polynomial, whats up with that?

[@ghazishaaban5253]

very good teacher

[@brianmclogan]

thanks! happy to help

[@postbarone]

what if you can't factor it? also, what (in your opinion) is the most difficult thing about pre-calc after finishing algebra2? I'm taking a pre-calc final without having taken the class because I want to skip the class and go straight to ap calc. I heard most of pre-calc is basically algebra2, therefore I need to know what new things I need to learn. any advice you would give me? thanks

[@brianmclogan]

I think if you knew these three chapters really well you would do fine in calc. Trig, you have to know your trig, rational function, you need to know rational functions, logarithms, especially natural logarithms and exponential. You are correct that most of Pre-Calc is Algebra 2 but it also serves another purpose and goes deeper than Algebra 2. If you feel comfortable in your math skills and are willing to work hard in Calc you can do it. However for a lot of people taking an extra year to focus on Pre-calculus skills is necessary to be successful in Calc. It might be helpful to speak with your Algebra 2, Pre-Calc, and Calc teacher for their advice as well as to maybe give you an assessment to see where you stand

[@postbarone]

Brian McLogan ok thank you! I'll be taking an assessment in a couple of days and if I pass I can go to ap calc next year. Also what in your opinion are the best ways to study this?

[@Orcrin12]

So say you have access to a graphing calculator, how do you determine the imaginary zeros? Can you do it using the graph or do you have to use rational zero test and factoring?

[@brianmclogan]

graphing calculator is not going to help you with the imaginary, that will come from factoring down your remaining factors

[@ghorg1337]

im only in first year of highschool and this might be a stupid question but when u set z^3-2z^2+2z-4 where do u get the -2 in -2z^2 from i understand the rest of it but i cant see where u get that

[@brianmclogan]

I don't see the -2

[@ghorg1337]

OriGinal Bosnian i looked it up now and i saw that u dont have the same school categorys as we do and translated to ur school system im in 3rd year of highschool but in our system its first of a 3 year school the first year after like basic school

[@ghorg1337]

Mr. McLogan's Math Channel i understood why u put -2 now at 6:16 its becasue of the polynoma system thing

[@brianmclogan]

okay good, glad you were able to have it straighten out

[@proshidhhajong9914]

Thank you Sir it was really helpful!

[@brianmclogan]

awesome! happy to be able to help

[@xbz3795]

what math level is this? algebra 2?

[@berekettibebu6904]

hello i am surprised to see ppl from uni here , me is learning this at grade 10 is kins of crazy

[@kumarshrey5206]

Thank you sir .....do u have any trick to solve using differiation calculus...plz reply...From india

[@brianmclogan]

I have plenty of videos on that, not tricks but examples

[@jlitt]

You are an angel

[@harrisonbennett7122]

Thank you

[@to0ot512]

why did u use -1 ? I tried to use you way at this polynomial and I couldn't make it find the zeros : x^3-7x^2+7x+15 how can u solve it by using the possible rational zeros ? and thank u so much

[@brianmclogan]

I would not use the rational zero test, I would graph it on my calculator or google to determine one rational zero, then use synthetic division to find the rest. -1, 3, and 5 look good

[@holyshit922]

On youtube Hindus (Indians) present general way to find the zeros of fourth degree polynomial First is based on factorization into two quadratics , second is the extension of this one which works for third degree polynomial

[@steamline432]

Awesome video, very helpful, but I spent an unholy amount of time trying to figure out why he said "q", then wrote an 8. I'm pretty dumb sometimes.

[@musicisthefoodofthesoul]

Super

[@VardhanAditya]

can you solve m^3 -3m^2 -4m +8

[@pgbrandon]

Any luck? I was trying to solve the same one;)

[@adarshkumar6231]

Omg nice!!

[@brianmclogan]

thanks

[@neil6257]

triggered

[@brianmclogan]

?

[@RzVids]

Brian McLogan hahaha, he meant that the student wasn't paying attention and you got peeved about it, thus you were "triggered".

[@gurpreetbhullar2540]

Pls make a video on. Eight power equation

[@brianmclogan]

that does not seem very fun, the same process would apply but there would be 8 zeros so a bit of work

[@gurpreetbhullar2540]

Brian McLogan sir I am unable to solve eight power equations do you know how to solve them. Pls help me it will great help sir

[@gurpreetbhullar2540]

I have four equations on eight power which I am unable to solve pls guide me sir

[@prathameshvarma4999]

Helped me a lot... Thanks!!

[@brianmclogan]

you are very welcome!

[@gerhardvanniekerk3759]

Pleas do -20x to the power of 4 + 5x to the power of 3 +17x to the power of 2 -129x +87 = 0

[@brianmclogan]

sorry only have time to work problems for my classes

[@wexer82]

Thank you.

[@brianmclogan]

+wexer82 you are very welcome! happy to help

[@rababbouali4023]

Can you find the zeroe of. 2x⁴-9x³+8x²-9x+2

[@kelaahmetaj785]

Your video was helpful for me, but I wanted to ask you about sth: how did z+1 came out as a factor. The other factor is taken by the coefficients we take by the synthetic division, but I wanted to know more about the first one

[@kevin_vr17]

Well, you get there by realizing that you're looking for zeros in the factor, so if z+1=0, z must equal -1 (subtract 1 from both sides)

[@kevin_vr17]

And he decided to start from ±1 as well. He could still get there by taking any of the other coefficients

[@ashutoshyadav667]

Sir I am from India and can't understand your language

[@nathanselman.realtor]

What do you do if your "q" doesn't equal 1?

[@brianmclogan]

then you use the factors of q

[@nami_lee8060]

What if the highest degree is 6?

[@imranali-iy5wk]

please make video on probability

[@brianmclogan]

I only have a couple videos, here is the playlist kzbin.info/aero/PL0G-Nd0V5ZMqm0bjCCiqbTCXQ2OzU2fqy

[@-clipz-]

God bless agtg

[@d111z]

لو سمحت لو تحط ترجمة تحت كل شرح اكون لك من الشاكرين شرح عربي

[@meownamejeff]

says "q" writes "8"

[@gnarlyarly9943]

Yosef it’s a q with a tail

[@fahadimran6961]

Sir how to solve x^4+x^3=0

[@brianmclogan]

factor out a x^3

[@sreejareddygummi4900]

-1 and 0,0,0 are zeroes

[@kfjfkeofitorhf9520]

X=-1 1+(-1)=0 X=0