There are lots of ways to do these. You can use the factor theorem and then polynomial long division, you can use the sum/product formulae for polynomials (sum of the roots of a cubic equal -b/a, product of the roots equal -d/a etc) and sometimes you can even use trigonometry. The cubic formula is only really used to completely brute force it if nothing else is working.
Best way to solve such questions is determine one root then use synthetic or long division to get rest of them Here -1/3 is a clear root as 3(-1/3)^3+(-1/3)^2-15(-1/3)-5 = 0 And then do synthetic division, Of main eq with (x+1/3) factor You get 3x^2-15=0 X = +√5, -√5, -1/3
That makes no sense at all. I have no idea what your teachers are teaching you. A difference of two perfect squares almost screams to be simplified more. It leaves the final result in its most simplest form.
And be not conformed to this world: but be ye transformed by the renewing of your mind, that ye may prove what is that good, and acceptable, and perfect, will of God. Romans 12:2 KJV Jesus saves..
There also is a cubic formula. As an example: x^3 - 9*x + 28 = 0 D = -9^3/27 + 28^2/4 = 169 x = cbrt(-28/2 + sqrt(169)) + cbrt(-28/2 - sqrt(169)) x = cbrt(-1) + cbrt(-27) x = -4
Why don’t we stop at x^2 - 5? I don’t usually see irrationals in factors; or complex numbers either. But this method does help in identifying the roots without needing the quadratic formula.
Oh easy factory by first doing X^2(3x+1)-5(3x+1) (X^2-5)(3x+1) You could factor more and could make it (sqrt(5)^2) and be a different of squares (X+sqrt(5))(x-sqrt(5))(3x+1) But also this is a very lucky problem with having just 3x+1 since if you had a different set then it becomes way longer to factor
(X-3)(X-6) Multiply it out and you get X^2-9X+18 There is a nice method called the ac method from some textbooks which motivates you to factor by grouping. ax^2+bx+c is a general form of 2nd degree polynomials where a,b, and c are real numbers, otherwise known as coefficients. Look at the factors of a and c multiplied together Which is 1*18=18 where a=1 and c =18 From here, choose from the factors of a*c=18 and find the factors that add up to the middle coefficient b=-9 The factors to choose are -3 and -6 because (-6)*(-3)=18 and (-6)+(-3)= -9 From here, you can rewrite x^2-9x+18 as x^2 - 6x - 3x + 18 and can factor by grouping as this video shows. Hope this helps
No in india this is not called middle term split it is called common method only . Though for cubic polynomials we use middle term splitting but this solution is by common method . In middle term splitting we do something different.
Why would you factor with the difference of squares on x^2-5? 5 isn't a perfect square, adding square roots into the polynomial gets confusing and it is pretty useless.
5 is still root(5) Multiplied by root(5) Perfect squares are associated with whole numbers, moreover they are associated with the natural numbers Any real number is still a square of another number Root(pi) is also a real number, and when you square it, it becomes pi But non of these numbers are natural numbers
Side effect of not studying maths in India 🤣🤣 that's why he is solving these types of question on TH-cam! But don't worry i will ask CBSE to allow you to become student of class X .
Only part I don’t understand is can you really do difference of squares if y in this case is not squared in the actual formula or does it not matter. Oh i see basically no matter what I guess you have to take the square root of what’s in those parentheses.
I'd try the Rational Roots theorem to see if ±1, ±5, ±1/3 or ±5/3 are solutions and we quickly see that x = -1/3 is a solution, so 3x + 1 is a factor. So, we can divide 3x + 1 into the cibic equation and find the quadratic term, and then it is easy to see the other two roots.
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It was lucky that 3x+1 was a common factor, presumably that was the key.
Yeah otherwise we would have to the long ass method
@@Laptopsigmagamer frrr
@@Laptopsigmagamer what method?
@@shiizu. the remainder theorem
@@tarushiagarwal4276no the dividing thing get one of the real roots then use synthetic division etc.
Watching from India 🇮🇳
Watching from south africa 🇿🇦
Watching from Pakistan
This guy teaches better than our school teachers @@AlphaSigmaGaming
Me from india
@@ZxDON.Real😢
I doubt if that method applies to every third-degree polynomial.
It doesn't.
Only if the ratio between the first degree and the second degree is the same as the ratio between the third degree and the fourth degree.
There's a cubic formula but... Let's NOT get into it, you'll have nightmares.
It doesn't
Sometimes you need to do more than 5 grouping just to find few solutions
There are lots of ways to do these. You can use the factor theorem and then polynomial long division, you can use the sum/product formulae for polynomials (sum of the roots of a cubic equal -b/a, product of the roots equal -d/a etc) and sometimes you can even use trigonometry. The cubic formula is only really used to completely brute force it if nothing else is working.
Best way to solve such questions is determine one root then use synthetic or long division to get rest of them
Here -1/3 is a clear root as
3(-1/3)^3+(-1/3)^2-15(-1/3)-5 = 0
And then do synthetic division,
Of main eq with (x+1/3) factor
You get 3x^2-15=0
X = +√5, -√5, -1/3
I wish JEE, ISI, IOQM, VITEEE, NEST asks these type of questions.
Bro 😂😂....
EGE
Send it to NTA!
AIR1 IITB CSE😂
Imagine AIR 247 reading this comment 🤣🤣
I hope these sums come to my Indian University exams 😂😂
Bro😂
No one cares about your university
@@samiatabassum9463 no one cares about your opinion either 😂
@@anmol-e7u okay little minded hobgoblin
@@anmol-e7u yoo bro 💀💀💀
I just learned this in algebra 2. Except unless it's a difference of two PERFECT squares we don't factor it more
That's what i thought too, but personally works for me bc i realise school could ask for me 3 factors and not just 2 anyways lol 😂 works in that case
Same but I learned in 7th honors algebra
That makes no sense at all. I have no idea what your teachers are teaching you.
A difference of two perfect squares almost screams to be simplified more.
It leaves the final result in its most simplest form.
Your handwriting is good
Ans:(x²-5)(3x+1)
I was curious how this solved in TH-cam shorts.
If youre gonna factor the x^2-5 you might as well pull a three out of 3x+1 so all the factors in parens are in terms of the roots of the polynomial
😊😊😊😊
😊
watching from Bangladesh 🇧🇩 ❤
Polynomiuuuhhl. Tree treee treeeeee.
And be not conformed to this world: but be ye transformed by the renewing of your mind, that ye may prove what is that good, and acceptable, and perfect, will of God.
Romans 12:2 KJV
Jesus saves..
💛Nice method 🧡💥💫
Grear explanation. This is a simple as it can get
Thanks!
Thank you bhaiya ❤
This only works if it nicely factors. Otherwise its algebraic long division and guessing the initial root
There also is a cubic formula.
As an example:
x^3 - 9*x + 28 = 0
D = -9^3/27 + 28^2/4 = 169
x = cbrt(-28/2 + sqrt(169)) + cbrt(-28/2 - sqrt(169))
x = cbrt(-1) + cbrt(-27)
x = -4
@@carultch that's a depressed cubic.
Wow what a good explanation 😮
Thanks dude 😎
Why don’t we stop at x^2 - 5? I don’t usually see irrationals in factors; or complex numbers either. But this method does help in identifying the roots without needing the quadratic formula.
You are supposed to stop at that. I don’t know why he continued.
Meanwhile indians and South Koreans kids be like ..... Why he lifting pen for such an easy question
Then please solve this by using this method : factories: a^3-6a^2+11a-6
Very very thanks. I was struggling in this problem but your solution gave me an idea about this. Thank you once again. 😊😊😊😊😊😊❤❤❤❤❤❤
Nice handwriting ❤
I had a mini heart attack when I heard "3x+1"
Nice method dude
Keep it up
Thanks you have made my doubt a huge doubt
Bro you made me understand this shit thanks bri
thankyousomuch! I was trying to solve question for hours and your this method just help me out thankyou
Bro just showed me how to solve my calculus problems in a simple manner without banging my head against the wall, I appreciate it🐧
Indians🗿
👇
Incredible🔥
When you know what’s 3x+1 really about
You can already see that this is one of the easier to factor 3rd degree polynomials
Nice explanation sir🎉
Oh easy factory by first doing
X^2(3x+1)-5(3x+1)
(X^2-5)(3x+1)
You could factor more and could make it (sqrt(5)^2) and be a different of squares
(X+sqrt(5))(x-sqrt(5))(3x+1)
But also this is a very lucky problem with having just 3x+1 since if you had a different set then it becomes way longer to factor
Hi , how do you do
x^2-9x+18
(X-3)(X-6)
Multiply it out and you get X^2-9X+18
There is a nice method called the ac method from some textbooks which motivates you to factor by grouping.
ax^2+bx+c is a general form of 2nd degree polynomials where a,b, and c are real numbers, otherwise known as coefficients.
Look at the factors of a and c multiplied together
Which is 1*18=18 where a=1 and c =18
From here, choose from the factors of a*c=18 and find the factors that add up to the middle coefficient b=-9
The factors to choose are -3 and -6 because (-6)*(-3)=18 and (-6)+(-3)= -9
From here, you can rewrite x^2-9x+18 as
x^2 - 6x - 3x + 18 and can factor by grouping as this video shows.
Hope this helps
no bro , this method are apply in only few questions but not in all questions lik3 ::-- x^3-3x^2-9x-5 and many more........
How do we do these types please
Great 👍
It's an amazing method to solve the problen
Thanks a lot ❤
It all went to shit when they introduced Alphabets to math...
After 12 hours of work, six hours of derivative exercises in math... I can tell you that my brain is now broken lol
Mf taught me more than math teacher in 20 seconds
that's wrong , it's just a designed example to get (x+3) a common factor
You learn math mostly by doing exercises yourself, not from listening to others
Thank you sir❤
- FROM INDIA
I am glad to find a very good explanation video 🤩🤩
Thanks!!!!
Thank you ❤
thanks i need this so much thanks
Can you also solve it by using Bézout's theorem?
sometimes this method is just confusing so better do synthetic division.
Where did you get the one from?
I live in India we learnt this in 5 th grade 😂
Best way
Thank you🙏💕❤
Excellent
To teach the method, you have to card stack by creating a workable polynomial before you turn the camera on. 😅
In my country INDIA it is middle term split bro .
No in india this is not called middle term split it is called common method only . Though for cubic polynomials we use middle term splitting but this solution is by common method . In middle term splitting we do something different.
Polynomialllll😮
Man everytime I see these, it looks like gibberish. But as he starts working them out, I begin to remember doing this shit in hs lmao
Thank you sir
My teacher would have deducted points, as 5 is not a perfect square.
That`s bs, technically any number in existence is a square of another number so that is correct
You never leave the answer as a perfect square though
Nice 👍
thank you
Lol, maths be like- u can't make fun of me
Factoring by grouping method
Amazing 👍
X^3-8x^2+4x+48=0
Maza a gyoo
just use foil..
Thx
Factorization is one of the most easiest chapter ever
99% Indian students 😂
Why do people make it more complicated than it has to be?
thanks bro
Don't you need both terms in the binomial to have a square root non-involving decimals for it to be a perfect square?
Why would you factor with the difference of squares on x^2-5? 5 isn't a perfect square, adding square roots into the polynomial gets confusing and it is pretty useless.
5 is still root(5) Multiplied by root(5)
Perfect squares are associated with whole numbers, moreover they are associated with the natural numbers
Any real number is still a square of another number
Root(pi) is also a real number, and when you square it, it becomes pi
But non of these numbers are natural numbers
This is basic 9th grade question.
Does the square root is applicable? Why can't just write (x+5)(x-5)?
Cuz (x+5)(x-5) = x^2 - 25.
Using a^2 - b^2 = (a+b)(a-b), a = x and b = sqrt(5) since sqrt(5)^2 = 5
(3x+1)(x^2-5)=(3x+1)(x-√5)(x+√5)
Thanks sir
I can't understand for your solution
How would you factorise cubic which has 1 or more complex roots🙄
I am an Asian and I learnt it at 13. I already know it. But, the way he teaches is realy great.
Who gives a shit.
Side effect of not studying maths in India 🤣🤣 that's why he is solving these types of question on TH-cam! But don't worry i will ask CBSE to allow you to become student of class X .
Only part I don’t understand is can you really do difference of squares if y in this case is not squared in the actual formula or does it not matter. Oh i see basically no matter what I guess you have to take the square root of what’s in those parentheses.
Simple
Perfect
Nice
how to factorize x³-x²-17x-15
(x+1)(x+3)(x-5)
We are studying it in class 8th of India
thanks
it was very easy
Bro wrote the best root sign
I wanna kiss this guy that was helpful
I'd try the Rational Roots theorem to see if ±1, ±5, ±1/3 or ±5/3 are solutions and we quickly see that x = -1/3 is a solution, so 3x + 1 is a factor.
So, we can divide 3x + 1 into the cibic equation and find the quadratic term, and then it is easy to see the other two roots.
Hey man try to be patient
This is the easiest thing ever.
🎉 good sir
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