Surprisingly Long Math Problem

[@rninness]

Orange! Ok I’m going to go buy a high school math textbook and brush up. It’s been too long since I’ve done this.

[@aidendoesstuff185]

NO WAY YOU LIKE ORANGE TOO?!??!!??!?

[@lucarroba]

Orange fucking rules 🔥🔥🔥🔥☝️

[@muhammadajmal6666]

kzbin.info/www/bejne/p2iwXoeih86ihtEsi=qOYCl3JEzo6-NzcP

[@poopyfarts42069]

@@lucarroba WE BE MAKING OUT OF THE HOOD WITH ORANGEE 🗣 🗣 🗣 🗣🔥🔥🔥🔥

[@keeplearningwithGoodguy]

Santra

[@blueberrypie3141]

it's really nice to see how you solve it differently than I was taught in Brazil (where I live). for example, we don't "subtract/divide both sides", we essentially do the same things but we say we are swapping the term side (and changing the operation, so obviously 2x = 8, and we bring the 2 that is multiplying to the right side, where it now divides, so x = 8/2 = 4). we also call the quadratic formula Bhaskara's formula for some reason. anyways nice video!!

[@jamasa007]

Where i'm from the quadratic formula is called "the second degree polynomial's solving equation".

[@blueberrypie3141]

@@jamasa007 omg that's so long 💀

[@jamasa007]

@@blueberrypie3141 its only 4 words in my language

[@samarrawal711]

It is called 'Dharacharya vidhi' here

[@PabloLacerdaPereira]

The bhaskara thing is an mistake that someone made more than a hundred years ago that became popular, probably cause it’s way better to say bhaskara than “fórmula do polinômio de segundo grau”

[@beanie8923]

Blue-green. I haven't needed to do math problems in years, but I still love your videos. I even vaguely remember some of the things you talk about. 😆

[@anubhavsingh2447]

blue. i cheated a little by checking for the pythagorian triplet 6-8-10, and substituted for x accordingly. got x = 11 on my first try!

[@er.logeshwarangs9129]

it's not cheating, its clever way of solving, i did the same 😂😂

[@ajaxjaiswal3442]

Lol me too, i guess we Indians are taught to go through problems fast. When I saw quad equation going in higher degrees, i went back to the problem again and solved it instantly using Pythagorean triplets. 😂

[@RockSaysPaperOP]

I did the same thing. By 3:40 the process devolved into a glorified guess-and-check anyway on the assumption that the solution was a rational number, which is no different than what we did. He might as well have applied that reasoning much earlier in the process and done this far faster, and without needing the rational root theorem. He technically assumed it was merely rational, not a whole number, but it was an assumption nonetheless and much more work.

[@Z-eng0]

Well, personally, I did synthetic division and tried 3 and 11 on my first tries (tried -3 in between but knew it probably wouldn't work anyway) cause I did the whole thing with no calculator so lucky me I guess (he could've simplified the expression after finding the x=3 root instead doing the long division on the big expression unnecessarily though)

[@someweirdstuff1256]

the question would be 10 times faster if the question stated “x is a positive integer” 😂

[@shivtheunknown]

nah, length of side cannot be negative by default there is no need to state that

[@someweirdstuff1256]

@@shivtheunknown I mean there is abstract geometry

[@misteroking]

@@shivtheunknown It's not about the positive but the integer part. There would be only 11 different possibilities if it said that

[@Cen_t1369]

nope, if x is a integer than you can immediately tell from the (x-3),y,10 triangle that it is a 8,6,10 triangle hence x=8+3=11@@misteroking

[@leolacic9442]

[@udaykumarsingh9130]

You should use a method this method worl like let the polynomial equal to any function called P(X)and just replace x with the numbers are you using for example Let a polynomial x^2+2x+1 We know that one of root is 1 We just check it out by just replacing x with the numbers negative 1 because one of the root is 1 then X+1=0 so,x=negative 1 that's the reason we replace x with -1 Just check it out now P(x)=x^2+2x+1 P(-1)=(-1)^2+2(-1)+1 =1+(-2)+1 =0 5:09

[@PJCatania]

Blue/green. Your videos are helping me brush up on the basics in preparation for having to help my kids with their math homework

[@SuPz3]

It could be shortened if you find the C for the big triangle and substract with x and then put it into the c^2=a^2+b^2 formula and it wil be like this 100=(x-3)^2 + (( surd 2x^2+2x+25)-x) and you will get x=11

[@ashokforklift8207]

Exactly what I did

[@jeyronokal1506]

Blue man 7:00 love your videos keep posting more of them pleass

[@MaciejGomoka]

Blue, I couldn't stop watching you smashing these big numbers, that were supposed to destroy our will to live. Thank you for this.

[@omnipresent_lightbulb]

Dark blue, I haven't stopped watching your videos lately! I love how you explain in an efficient and intuitive way

[@drakkondarkspell]

Puce. Because no one ever says puce is their favorite color. It's too purple to be pink and too pink to be purple. How exciting.

[@elvkim96]

Purple, your videos are helping me see problems in different perspectives and I realized that they're not all that hard!

[@coopersmith3182]

Green. These are really enjoyable! I'm thrilled I found your channel

[@klassmagicker]

Red! Awesome video, any polynomial above a degree of two just makes me want to cry. As an aside, I was working on this problem that asked how many factors a certain number had (it was some highly composite number, I want to say 600?) My immediate thought was to get the prime factors and count from there, as you did in the video. But I was having some trouble with the combinations. Maybe I'm just a bit rusty and need to relearn my combinatorics, but do you have a suggestion on how to go about it?

[@fe255]

First find the prime factors. 600 has a prime factorization of 2^3 * 3 * 5^2. Every factor will be a combination of these prime factors. Each prime factor has 1 plus its exponent as the number of ways you can add it into a factor (0 copies, 1 copies, 2 copies, etc.), so you can use the fundamental counting principal. In this case you would get (3+1)(1+1)(2+1)=4*2*3=24 factors. Hope this helped. I could provide some clarification if this was not clear.

[@loloooooooooooooo]

Aqua Green. I'm flabbergasted how this channel doesn't have a million+ subscribers. Andy you're such a smart and intelligent guy. Sorry if my english was bad, but you did a great job!

[@raulbenavides8291]

Blue/green! Great walk through defintely do more of these

[@jreese8284]

All of them! Thanks for your work!

[@jaja47_coolness]

Oh my God, literally today I was working on a problem and realized I could use the Rational Zero Theorem but I didn't remember it, and couldn't find anything in writing that I could understand. However, seeing it actively performed in front of me really helps with that! I also didn't realize, but I guess I needed a refresher on polynomial long division! Oh and if you're curious, the math problem was: "A+B+C=1 A²+B²+C²=2 A³+B³+C³=3 What is (A,B,C)?" I'm only using algebra and so far that's been cruel, I'm seven pages into it and probably inefficiently solving it, but I'm doing it until I got the answer without a calculator for some reason!

[@jeremiahlundquist1932]

Orange. Because of your videos I'm starting to realize that mathematics is about have more and more weapons (formulas) in your toolkit and being creative with where and how to apply them. A 3,000ft view that I never recognized when studying math in school. Thank you for this window into the next level of understanding mathematics.

[@cameronhauberg5026]

marooooon! this one was really exciting. so cool to see you be able to see the steps real quick.

[@naziaparveen2516]

Teal! Despite being long and tedious you still managed to make it seem fun. How exciting!

[@Theepicspartan55]

Olive drab I only just found your channel and your problems prove to be very fun to do as an activity

[@nandisaand5287]

I did it sort of in my head when I realized there qas going to be an x^4 polynomial, and didnt even consider going further.

[@killerbot1740]

Red brother REally enjoy watching your videos and made me like solving maths related problems a lot.

[@zeddoes]

Purple. I used to do math when I was stressed when I was a kid. This reminds me that times

[@Quizlz]

Blue. I got to the part where it was a quartic polynomial, but I forgot the p/q stuff and gave up (either way I wasn't checking for 36 factors). I also forgot side lengths couldn't be negative for a second and did the whole thing twice, but assuming 'a' was the negative version of that radical.

[@tunneloflight]

Red, though I first worked through all the ways to use quadrilateral formulas. The other missing side length is non integer and made a hash of things. Doing the quadrilateral area formula against the sum of triangles became a mess. Discarding that I did as you dud in a more convoluted way. Rather than struggling through finding the roots of the quartic, I threw it into a spreadsheet, plotted and quickly solved it that way. Though not proper for this sort of solution, 50 years of engineering on - I use them a lot to bash through problems. But then too, I tend to solve for all of the missing elements and nit just the one sought in the problem statement. Force of habit.

[@vinhhiennguyen-y2k]

Blue-ish grey, what a splendid mathematical approach to this problem!

[@mrbagginz5963]

im only a 6th grader and this is fun and you explain it very well

[@GileadMaerlyn]

I have discovered your videos recently, and I noticed you always detail how you get from (a+b)² to a²+2ab+b². I don't know in your country, but in France we are taught what we call "identités remarquables" (remarkable identities) that we are supposed to know: (a+b)² = a²+2ab+b² (a-b)² = a²-2ab+b² (a+b)(a-b) = a²-b²

[@jjacobsnd5]

I think he's from America, and we also learned those identities! I think he just prefers to show (basically) every step in these videos.

[@CoderGautam]

even in india

[@IshaanSainii]

Apprendrez-moi le français(i say this to every french person)

[@hidoshi1994]

It just speeds up the process knowing these identities, I guess Andy details every step for learning purposes

[@kaifalcone8025]

Light green! These videos are making me very excited to teach geometry one day

[@cmms]

At this type questions i first check if there is a special triangle. (3-4-5, 5-12-13, 8-15-17, 7-24-25) Difference of big triangle's edges is 7. so i tried 8 15 17 triangle and it fit perfectly.

[@Canzandridas]

For the first time I'm gonna pause lol. The triangle with hypotenuse 10cm means the sides are 8 and 6; 64 plus 36 is 100 which are the squares. Since the side that's 8 is x-3 then x=11 (8+3). Unless I'm missing something (which is what I'm guessing) or you're going for a longer route I don't see where it's long Ok I like the longer method but since the result is the same I'd say I prefer the shorter route lol

[@Pyladin]

What if the side you think is 8 is in fact 6? You will have to test for that?

[@guffels]

Pretty sure you know from the beginning that x is 9 or 11 because the 10 hypotenus makes the first triangle a special right and the known side has to be 9 or 11. From there you take 9 and assume a is 8 or take 11 and assume a is 6. Then pothag the big triangle to check whether the hypotenuse equals x+6 or x+8

[@ml09394]

Purple, this was really good. It would be cool to have a test that's like one massive question like this. except I realized there's a big issue if I'm wrong

[@darkviking7135]

Purple. This felt like watching a magician keep pulling handkerchiefs out of their sleeve.

[@clblowe]

Green! That was a terribly tedious one, but always fun to watch you solve it!

[@ParallaxRS]

Teal - Im slowly falling back in love for pure mathematics after being a pi=3 engineer for 10 years

[@cuecadelacut]

By the end I would have forget what I was looking for

[@lonelysonofgod97]

this is more fun than sport

[@kavitanidhi8810]

Pink! This problem was a rollercoaster but so exciting!

[@narwaffl]

At first sight the diagram reminded me of the proof for sine of summed angles

[@PhilosophicalNonsense-wy9gy]

a variable a was chosen but a could actually be determined by using pythagorean theorem on the bigger triangle

[@mujaheedgoni9712]

Dark blue, I don't think I am sane enough to do this but I am stupid enough.

[@clif18h]

Yellow. Thank you for the fun question and clear illustration . Love this channel

[@mikaeloverfjord9047]

I got the correct answer WAY faster, although I made an assumption. That the bottom left triangle was a scaled version of the 3, 4, 5 right angle triangle. (with all sides being double) Which was a good assumption if the problem was gonna have a nice solution. 😂 And fav color is blu

[@AtalaShalash]

After I saw the triangle with c=10 I just knew x was either 9or 11 since you need legs 8 and 6 to get a hypotenuse of 10, and plugging in those two x values into x gives you 8 or 6

[@arxeha]

mint! at that point where there are too many x inside the equation i would probably just look at the multiple option and try the answer one by one see which one is correct

[@Gamert80]

At the end you could have said "How Thrilling".

[@khowe42]

Blue. That was some really tedious work. Good job.

[@AndyPanda9]

Purple! I hated math in school (back in the 50's and 60's - crappy teachers made math boring/confusing) -- but I love solving puzzles and I've always been good with all the sciences (except for the math part that I have just always avoided). Anyway - watching your videos makes math seem fun and maybe it's not too late for me to start learning math at 70 years old?

[@Toryou]

Light blue. You explained it nicely.

[@BlankTH]

You don't need to do long division and check the remainder when guessing roots. Just plug your guess into the polynomial and see if it is equal to 0.

[@divyanshsarvapriya]

The colour of your eyes 😳

[@Yareyare161]

Gray, nice videos. This videos would help me while reviewing for my subjs.

[@urble]

Cerulean, can you do a video on polynomial long division?

[@IndirectCogs]

Favorite color is purple. I think the one "early" math concept I really struggle with is long-division. I don't know why I got through the calculus battery in college it's just like OOF. When I saw long division I was like "oh god this is a problem I'd skip"

[@1959mikel]

Blue, how exciting… and long! Worth the wait.

[@farmcat3198]

Green. I'm about to retake all my maths. I appreciate your videos.

[@RyderChiang]

Light blue, you are an amazing KZbinr! Thank you very much!

[@VaahoFashionHouse]

Lilac is the most beautiful colour

[@TheMasterGreen]

respect for writing all that

[@DanielNRollins]

Purple. Definitely a bit involved but seems fun, and tedious.

[@clallseven]

Earth tones suit me. How exciting!

[@CubeATime-AKAEddieArtze]

Red! I love your channel! Keep up the good work

[@MathletebySaad]

Why didn’t you use factor theorem?

[@rowrow_]

Your content is gold!

[@johnpaauloo]

Blue from the Philippines, how exciting!

[@whocares_yes]

Light Blue / Teal! How exciting.

[@Peterledgend]

Blue, using synthetic division and the factor theorem would have probably made solving the polynomial much easier.

[@peilobsg4832]

If f(3)=0 that means that the reminder of dividing f(x) by (x-3) is 0, f(a) is a reminder of dividing f(x) by (x-a).

[@anonymousamateurph]

Blue! Love this problem! How exciting! 💙

[@thomasmackenzie5295]

Blue!　This brings back lots of memories. What fun.

[@cstuart5638]

Lime green, I find long division so much more tedious than synthetic division. I solved the 4th degree polynomial with synthetic.

[@Sergote12]

Blue. Where was these videos when I was about to take my exams? Anyways, love it!

[@moamel27]

‏‪3:28‬‏ what is the name of this method?

[@EdgarMkhitaryanH]

Amazing Videos Andy, thn a lot for awakening a long time sleeping knowledge in my brain :-) btw. that is the application you use to move around all the shapes and formulas so easily?

[@BederikStorm]

Why didn't you use Bezout theorem for the checking and long division only for cases when it's equal to 0?

[@erlanbek-kanybekov]

Why there's an extra "x" in √96 - x^2+6x ? 1:10

[@casanovatwentytwo]

orange, that was a whole journey omg

[@ericthetuber]

Black is too cool! Yo this was a journey. New here, absolutely love your content!

[@SarcasmoRex]

Green. This was just awesome.

[@johnporter7915]

Good problem, explanation and software 👍💯 thanks!

[@Bosiolio]

Blue. I love these videos. Reminding me of math I used to do so much faster!

[@foryx_]

Dark green. I just plugged mine into desmos lol. I think I went wrong somewhere during calculations. not dividing by two when I could overcomplicated a lot of it

[@CharlesB147]

Blue. And holy moly that was a slog all the way to the end.

[@lpzmarkus564]

I got a question At 5:58 he made the √60 into 2√15, idk how u get that at all so if someone could help itll be greatly appreciated

[@patriciamcglathery844]

Purple. Love your videos!

[@MrMike3137]

Red. Ouch! How exciting indeed. It's been so long. Thank you

[@thefondation2938]

Pink. My guy, you are the reason i don't have an f in Geo rn.

[@MikeSimoneLV]

Purple. This channel is great!

[@MatthewFarrugia18]

I watch these videos before I sleep, or instead of. How exciting.

[@ibaimartinituino7291]

Every one of them, specially blue green, pistachio green and light orange

[@ak_hian]

White, Blue, Black. Great Explanation by the way!

[@CptGallant]

Purple. I fell into the trap of thinking that those triangles on the left were similar because I assumed that was a right angle in the far left corner. It isn't. It's like 90.8 degrees.

[@dragoljubvujovic2325]

MAROON! And this one was a bit of a braintwister for me, I couldnt figure out what to do with it

[@redacted_to_surpass_metal_gear]

Once you had the 4th order polynomial, why not just use the quartic formula to find the roots?

[@saranshbharti7105]

The moment I saw 10cm, I immediately thought of 10,8,6 triangle, and hit and trial worked. Not a good way to solve, but kinda worked.

[@jenniferweaver9620]

Brown. I am working all of your problems and getting maybe 2% close!