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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#polynomials #brianmclogan

Пікірлер: 224

  • @brianmclogan
    @brianmclogan12 жыл бұрын

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

  • @iftikharshamsniloy8579

    @iftikharshamsniloy8579

    3 жыл бұрын

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

  • @Bigschmitt25
    @Bigschmitt258 жыл бұрын

    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

    @brianmclogan

    8 жыл бұрын

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

  • @brianmclogan
    @brianmclogan11 жыл бұрын

    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

  • @liankhai6019
    @liankhai60197 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    7 жыл бұрын

    here for you!

  • @mohammadshahade8753

    @mohammadshahade8753

    6 жыл бұрын

    what if she saw your comment ?

  • @darthsion3844

    @darthsion3844

    5 жыл бұрын

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

  • @annhashi1768

    @annhashi1768

    5 жыл бұрын

    Lol

  • @DennisBolanos

    @DennisBolanos

    4 жыл бұрын

    LOL.

  • @asystoleD
    @asystoleD7 жыл бұрын

    0:45 LMFAO

  • @brianmclogan

    @brianmclogan

    7 жыл бұрын

    haha some things never change

  • @bksupply8186
    @bksupply81865 жыл бұрын

    So lucky i found this channel

  • @deedeeOWL
    @deedeeOWL5 жыл бұрын

    👍🏼 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
    @Riverbend17523 жыл бұрын

    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

    @IRON_KING_KNIGHT

    2 жыл бұрын

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

  • @she8334

    @she8334

    Жыл бұрын

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

  • @souryour6598

    @souryour6598

    5 ай бұрын

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

  • @Riverbend1752

    @Riverbend1752

    5 ай бұрын

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

  • @brianmclogan
    @brianmclogan11 жыл бұрын

    I appreciate your kind words

  • @1v1noscope37
    @1v1noscope374 жыл бұрын

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

  • @mt33205
    @mt332054 жыл бұрын

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

  • @fedorshcheglov5534
    @fedorshcheglov55344 жыл бұрын

    Watching this during quarantine, very helpful when you can't reach your teacher! :)

  • @kmillz7414
    @kmillz7414 Жыл бұрын

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

  • @aliris19
    @aliris198 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    8 жыл бұрын

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

  • @khushibarnawal9271
    @khushibarnawal92716 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    6 жыл бұрын

    happy they help, visit them whenever you neeed

  • @Starscrayper
    @Starscrayper7 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    7 жыл бұрын

    happy to be able to assist you

  • @jesuisravi
    @jesuisravi5 жыл бұрын

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

  • @those.gamers.
    @those.gamers.5 жыл бұрын

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

  • @anjugupta25

    @anjugupta25

    5 жыл бұрын

    Taefan!

  • @jonathanjohnson7508
    @jonathanjohnson75089 жыл бұрын

    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

  • @yzel36
    @yzel363 жыл бұрын

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

  • @jerryfan8378
    @jerryfan83784 жыл бұрын

    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.

  • @cadmiumbop
    @cadmiumbop5 жыл бұрын

    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

  • @eunicedickson9526
    @eunicedickson95267 ай бұрын

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

  • @heystobit2608
    @heystobit26085 жыл бұрын

    Sir, can we use another method other than factorization.

  • @lanyahunar2659
    @lanyahunar26592 жыл бұрын

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

  • @gsbedi68
    @gsbedi684 жыл бұрын

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

  • @mammamia151
    @mammamia1513 жыл бұрын

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

  • @Hahaalot
    @Hahaalot7 жыл бұрын

    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

    @brianmclogan

    7 жыл бұрын

    happy to help

  • @gr8tmeg
    @gr8tmeg11 жыл бұрын

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

  • @Historyhappenshere
    @Historyhappenshere3 жыл бұрын

    Brian is saving my life right about now

  • @ansenliu
    @ansenliu3 жыл бұрын

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

  • @livfrazier6295
    @livfrazier62958 жыл бұрын

    Wow, this was explained so well. THANK YOU!

  • @brianmclogan

    @brianmclogan

    8 жыл бұрын

    +Olivia Frazier you are very welcome!

  • @thomasjones145
    @thomasjones1454 жыл бұрын

    Thank you, this helped me so much!

  • @Orcrin12
    @Orcrin126 жыл бұрын

    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

    @brianmclogan

    6 жыл бұрын

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

  • @ganeshnithiyananthan8487
    @ganeshnithiyananthan84873 жыл бұрын

    thanks for these videos really helped a lot for my exams

  • @darrelseibert420
    @darrelseibert4209 жыл бұрын

    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

    @brianmclogan

    9 жыл бұрын

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

  • @splabicado6510
    @splabicado65103 жыл бұрын

    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?

  • @annhashi1768
    @annhashi17685 жыл бұрын

    Thank you sir it really helped me .

  • @sethlangendoen1313
    @sethlangendoen13133 жыл бұрын

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

  • @FreeDomSy-nk9ue
    @FreeDomSy-nk9ue6 жыл бұрын

    The trick you mentioned about the constant is just amazing

  • @brianmclogan

    @brianmclogan

    6 жыл бұрын

    happy to help

  • @sohamparekh
    @sohamparekh4 жыл бұрын

    Very helpful, thank you.

  • @nonokay20
    @nonokay2011 жыл бұрын

    You are a great teacher!!!!

  • @legendneverdiegaminglndg4136
    @legendneverdiegaminglndg41363 жыл бұрын

    Sir can you tell me who was the student ?

  • @Its_A_Dulla
    @Its_A_Dulla Жыл бұрын

    Why is the q ±1?

  • @user-om3vf1qf2d
    @user-om3vf1qf2d7 ай бұрын

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

  • @monicamedina3838
    @monicamedina38385 жыл бұрын

    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.

  • @remytherat2175
    @remytherat21754 жыл бұрын

    THIS SAVED ME THANK YOUUU

  • @postbarone
    @postbarone7 жыл бұрын

    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

    @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

    @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?

  • @brianmclogan
    @brianmclogan11 жыл бұрын

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

  • @MPV2023

    @MPV2023

    6 жыл бұрын

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

  • @paulinjosepha2336
    @paulinjosepha23367 жыл бұрын

    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

    @brianmclogan

    7 жыл бұрын

    happy to be able to help you out!

  • @bluekai3317
    @bluekai33173 жыл бұрын

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

  • @RzVids
    @RzVids7 жыл бұрын

    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

    @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

  • @ShivaPrasad-hm5lk
    @ShivaPrasad-hm5lk6 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    6 жыл бұрын

    awesome!

  • @rolandpoland5363
    @rolandpoland53633 жыл бұрын

    Helped me pass too many Alg 2 tests

  • @dallasbakerfollowthecode
    @dallasbakerfollowthecode9 жыл бұрын

    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

    @brianmclogan

    9 жыл бұрын

    dallas baker at what time marker in the video?

  • @dallasbakerfollowthecode

    @dallasbakerfollowthecode

    9 жыл бұрын

    Wow not expecting to respond but hold on

  • @proshidhhajong9914
    @proshidhhajong99147 жыл бұрын

    Thank you Sir it was really helpful!

  • @brianmclogan

    @brianmclogan

    7 жыл бұрын

    awesome! happy to be able to help

  • @Jakomaniac1
    @Jakomaniac13 жыл бұрын

    Bless your soul

  • @xbz3795
    @xbz37953 жыл бұрын

    what math level is this? algebra 2?

  • @marymccory8075
    @marymccory80758 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    8 жыл бұрын

    +Mary Mccory here all year long

  • @shravanikharkar4687
    @shravanikharkar46873 жыл бұрын

    My teacher suggest me this channel To better understand 😊

  • @dailycam9579
    @dailycam95794 жыл бұрын

    Sir you are the best

  • @aadamrayanbinabu
    @aadamrayanbinabu7 жыл бұрын

    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

    @brianmclogan

    7 жыл бұрын

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

  • @900q8
    @900q8 Жыл бұрын

    tysm this helped a lot!

  • @ipihu
    @ipihu3 жыл бұрын

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

  • @JLvatron
    @JLvatron2 жыл бұрын

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

  • @to0ot512
    @to0ot5127 жыл бұрын

    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

    @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

  • @rababbouali4023
    @rababbouali40234 жыл бұрын

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

  • @harrisonbennett7122
    @harrisonbennett71225 жыл бұрын

    Thank you

  • @danpost5651
    @danpost56514 жыл бұрын

    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.

  • @nathanselman.realtor
    @nathanselman.realtor6 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    6 жыл бұрын

    then you use the factors of q

  • @Maharshigurukultrader
    @Maharshigurukultrader6 жыл бұрын

    (X-1)^4 + (x-5)^4 = 82 how solve it?

  • @oskarlindelof9685
    @oskarlindelof96857 жыл бұрын

    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

    @brianmclogan

    7 жыл бұрын

    you can do that too

  • @dash15yearsago67
    @dash15yearsago673 жыл бұрын

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

  • @ryanostertag3570

    @ryanostertag3570

    3 жыл бұрын

    bro we down bad asf rn

  • @boywonder_YT
    @boywonder_YT2 жыл бұрын

    Tristen, you really gotta listen buddy.

  • @Remarkpeace
    @RemarkpeaceАй бұрын

    Thank you isn't enough!

  • @kelaahmetaj785
    @kelaahmetaj7855 жыл бұрын

    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

    @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

    @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

  • @wexer82
    @wexer828 жыл бұрын

    Thank you.

  • @brianmclogan

    @brianmclogan

    8 жыл бұрын

    +wexer82 you are very welcome! happy to help

  • @kumarshrey5206
    @kumarshrey52066 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    6 жыл бұрын

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

  • @ghorg1337
    @ghorg133710 жыл бұрын

    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

    @brianmclogan

    10 жыл бұрын

    I don't see the -2

  • @ghorg1337

    @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

    @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

    @brianmclogan

    10 жыл бұрын

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

  • @jlitt
    @jlitt5 жыл бұрын

    You are an angel

  • @kushalchakrabarti240
    @kushalchakrabarti2405 жыл бұрын

    Sir.. big fan!

  • @brianmclogan

    @brianmclogan

    5 жыл бұрын

    cheers! happy to help!

  • @bustinbinden
    @bustinbinden3 жыл бұрын

    that chinstrap was STRONG

  • @brianmclogan

    @brianmclogan

    3 жыл бұрын

    Yeah old school

  • @Samsam_149
    @Samsam_1493 жыл бұрын

    ur a god dude thank you so much

  • @steamline432
    @steamline43211 ай бұрын

    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.

  • @prathameshvarma4999
    @prathameshvarma49997 жыл бұрын

    Helped me a lot... Thanks!!

  • @brianmclogan

    @brianmclogan

    7 жыл бұрын

    you are very welcome!

  • @ghazishaaban5253
    @ghazishaaban52536 жыл бұрын

    very good teacher

  • @brianmclogan

    @brianmclogan

    6 жыл бұрын

    thanks! happy to help

  • @devan7485
    @devan74852 жыл бұрын

    take in these kids are like 30 years old now

  • @neil6257
    @neil62577 жыл бұрын

    triggered

  • @brianmclogan

    @brianmclogan

    7 жыл бұрын

    ?

  • @RzVids

    @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".

  • @nami_lee8060
    @nami_lee80603 жыл бұрын

    What if the highest degree is 6?

  • @huankoi3403
    @huankoi34032 жыл бұрын

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

  • @VardhanAditya
    @VardhanAditya5 жыл бұрын

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

  • @pgbrandon

    @pgbrandon

    3 жыл бұрын

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

  • @ASTROvalo
    @ASTROvalo6 жыл бұрын

    Awesome

  • @brianmclogan

    @brianmclogan

    6 жыл бұрын

    thanks!

  • @musicisthefoodofthesoul
    @musicisthefoodofthesoul4 жыл бұрын

    Super

  • @meownamejeff
    @meownamejeff5 жыл бұрын

    says "q" writes "8"

  • @gnarlyarly9943

    @gnarlyarly9943

    4 жыл бұрын

    Yosef it’s a q with a tail

  • @d111z
    @d111z5 жыл бұрын

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

  • @holyshit922
    @holyshit9224 жыл бұрын

    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

  • @adarshkumar6231
    @adarshkumar62316 жыл бұрын

    Omg nice!!

  • @brianmclogan

    @brianmclogan

    6 жыл бұрын

    thanks

  • @samrudhibafna3962
    @samrudhibafna39623 жыл бұрын

    if f(x)be a polynomial satisfying f(x).f(1\x)= f(x)+f(1\x) and f(4)= 65 find f(20)

  • @jawaidahmed3453
    @jawaidahmed34535 жыл бұрын

    Consider a polynomial that don't has any of roots So this synthetic division is compromised

  • @pleasanttask8191
    @pleasanttask81917 жыл бұрын

    hey whats 3 to the power of 2 bc I'm dumb

  • @pleasanttask8191

    @pleasanttask8191

    7 жыл бұрын

    pls tell me cuz its easy

  • @pleasanttask8191

    @pleasanttask8191

    7 жыл бұрын

    well its easy to u.....

  • @brianmclogan

    @brianmclogan

    7 жыл бұрын

    3^2 means 3*3 which is 9