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.
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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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Пікірлер: 224
glad I could help, its fun when those things finally start to make sense
@iftikharshamsniloy8579
3 жыл бұрын
Thanks a lot ,sir. I really appreciate your effort ! You helped me a lot. May Allah bless you.
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
8 жыл бұрын
+Nick Meme you are welcome! yep it's the real deal, life in my classroom
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
LOL my math teacher is too lazy to teach so she told us to watch this video
@brianmclogan
7 жыл бұрын
here for you!
@mohammadshahade8753
6 жыл бұрын
what if she saw your comment ?
@darthsion3844
5 жыл бұрын
@@mohammadshahade8753 maybe it's not the real name? Lol
@annhashi1768
5 жыл бұрын
Lol
@DennisBolanos
4 жыл бұрын
LOL.
0:45 LMFAO
@brianmclogan
7 жыл бұрын
haha some things never change
So lucky i found this channel
👍🏼 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
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.
@IRON_KING_KNIGHT
2 жыл бұрын
I’m going through the same thing in differential equations as well 🤣🤣🤣
@she8334
Жыл бұрын
Are we living the same life? a sophomore too, and I am here because of my differential equations course
@souryour6598
5 ай бұрын
You learn this in collage, im learning it in year 9
@Riverbend1752
5 ай бұрын
@@souryour6598 I hope you are also studying English. One does not study at collage; they study at college.
I appreciate your kind words
Was going crazy trying to figure out how to factor these, appreciate the help 💪
I'm taking engineering and watching this guys vids for finals, really shouldn't have skipped so many lectures...
Watching this during quarantine, very helpful when you can't reach your teacher! :)
Brian, your videos continue to help me everyday. Thank you for doing what you do...and please continue to do so.
I'm a parent struggling to explain "CC" math to my kid and wow do I appreciate your videos. Thank you!!!
@brianmclogan
8 жыл бұрын
+Sara Roos you are very welcome! happy my videos are helping!
Sir your videos are easy to understand... I wish I could study with you in my school.
@brianmclogan
6 жыл бұрын
happy they help, visit them whenever you neeed
With your help, I'm able to cram for my college algebra test, and I am infinitely grateful for this.
@brianmclogan
7 жыл бұрын
happy to be able to assist you
Question: What do you call the course you are teaching here? Is it Algebra 2 or precalculus or what?
ah thank you, my math teacher expected us to do a packet with a question like this and didn’t teach it lol
@anjugupta25
5 жыл бұрын
Taefan!
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
Your channel is a life saver thank goodness I found these videos
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.
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
What if this method also doesn't work for me? I'm solving x^4 + 2x^2 - x - 3 = 0. Any help please?
Sir, can we use another method other than factorization.
What if you tried all number and not equal to 0 to factor it?? please answer
Wow !! Thank you for the help sir!! You were amazing !!
Thank you so much for helping me with my math homework!
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
7 жыл бұрын
happy to help
why in the beginging couldn't do you factor by grouping? you could group z^4 and z^3 together, and -2z and -4
Brian is saving my life right about now
Thank you so much, you're a good man, you deserve honor :)
Wow, this was explained so well. THANK YOU!
@brianmclogan
8 жыл бұрын
+Olivia Frazier you are very welcome!
Thank you, this helped me so much!
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
6 жыл бұрын
graphing calculator is not going to help you with the imaginary, that will come from factoring down your remaining factors
thanks for these videos really helped a lot for my exams
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
9 жыл бұрын
Darrel Seibert Good Luck! keep up the hard work and let me know how you do
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?
Thank you sir it really helped me .
All he said was "factor by grouping" in the beginning and I could solve my question.
The trick you mentioned about the constant is just amazing
@brianmclogan
6 жыл бұрын
happy to help
Very helpful, thank you.
You are a great teacher!!!!
Sir can you tell me who was the student ?
Why is the q ±1?
Can i ask what grade u teach it's very helpful
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.
THIS SAVED ME THANK YOUUU
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
7 жыл бұрын
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
7 жыл бұрын
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?
When graphing this polynomial see that there are no real roots. Meaning their are no real zeros you can solve for(x-intercepts)
@MPV2023
6 жыл бұрын
Brian McLogan ...can u find me the roots for below eq'n... s^4+12s^3+91s^2+150s+50....???
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
7 жыл бұрын
happy to be able to help you out!
this make me feel like im in actual class tho it's online class now bc of corona
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
7 жыл бұрын
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
superb excellent.......... I liked ur explanation continue
@brianmclogan
6 жыл бұрын
awesome!
Helped me pass too many Alg 2 tests
Hey im taking college algebra and I havnt taken a math class sense junior year of highschool and I remember this but im not understanding how you went from a x^3 to a square?
@brianmclogan
9 жыл бұрын
dallas baker at what time marker in the video?
@dallasbakerfollowthecode
9 жыл бұрын
Wow not expecting to respond but hold on
Thank you Sir it was really helpful!
@brianmclogan
7 жыл бұрын
awesome! happy to be able to help
Bless your soul
what math level is this? algebra 2?
Great!!!!! I should have came here for help a long time ago!!!!!
@brianmclogan
8 жыл бұрын
+Mary Mccory here all year long
My teacher suggest me this channel To better understand 😊
Sir you are the best
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
7 жыл бұрын
sorry I do not have time to work on extra problems for students as I receive multiple requests
tysm this helped a lot!
Thanks you helped a lot I want tutions from you if you can plz
Great explanation! And who are the fools at 0:42 disturbing class!!
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
7 жыл бұрын
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
Can you find the zeroe of. 2x⁴-9x³+8x²-9x+2
Thank you
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.
What do you do if your "q" doesn't equal 1?
@brianmclogan
6 жыл бұрын
then you use the factors of q
(X-1)^4 + (x-5)^4 = 82 how solve it?
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
7 жыл бұрын
you can do that too
6:17 wouldn't we have to use rational root theorem again?
@ryanostertag3570
3 жыл бұрын
bro we down bad asf rn
Tristen, you really gotta listen buddy.
Thank you isn't enough!
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
Ай бұрын
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
Ай бұрын
And he decided to start from ±1 as well. He could still get there by taking any of the other coefficients
Thank you.
@brianmclogan
8 жыл бұрын
+wexer82 you are very welcome! happy to help
Thank you sir .....do u have any trick to solve using differiation calculus...plz reply...From india
@brianmclogan
6 жыл бұрын
I have plenty of videos on that, not tricks but examples
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
10 жыл бұрын
I don't see the -2
@ghorg1337
10 жыл бұрын
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
10 жыл бұрын
Mr. McLogan's Math Channel i understood why u put -2 now at 6:16 its becasue of the polynoma system thing
@brianmclogan
10 жыл бұрын
okay good, glad you were able to have it straighten out
You are an angel
Sir.. big fan!
@brianmclogan
5 жыл бұрын
cheers! happy to help!
that chinstrap was STRONG
@brianmclogan
3 жыл бұрын
Yeah old school
ur a god dude thank you so much
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.
Helped me a lot... Thanks!!
@brianmclogan
7 жыл бұрын
you are very welcome!
very good teacher
@brianmclogan
6 жыл бұрын
thanks! happy to help
take in these kids are like 30 years old now
triggered
@brianmclogan
7 жыл бұрын
?
@RzVids
7 жыл бұрын
Brian McLogan hahaha, he meant that the student wasn't paying attention and you got peeved about it, thus you were "triggered".
What if the highest degree is 6?
i'm from vietnam and it's very simple here
can you solve m^3 -3m^2 -4m +8
@pgbrandon
3 жыл бұрын
Any luck? I was trying to solve the same one;)
Awesome
@brianmclogan
6 жыл бұрын
thanks!
Super
says "q" writes "8"
@gnarlyarly9943
4 жыл бұрын
Yosef it’s a q with a tail
لو سمحت لو تحط ترجمة تحت كل شرح اكون لك من الشاكرين شرح عربي
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
Omg nice!!
@brianmclogan
6 жыл бұрын
thanks
if f(x)be a polynomial satisfying f(x).f(1\x)= f(x)+f(1\x) and f(4)= 65 find f(20)
Consider a polynomial that don't has any of roots So this synthetic division is compromised
hey whats 3 to the power of 2 bc I'm dumb
@pleasanttask8191
7 жыл бұрын
pls tell me cuz its easy
@pleasanttask8191
7 жыл бұрын
well its easy to u.....
@brianmclogan
7 жыл бұрын
3^2 means 3*3 which is 9