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.
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.
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
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
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.
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.
(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
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.
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.
Watching from India 🇮🇳
Watching from south africa 🇿🇦
Watching from Pakistan
This guy teaches better than our school teachers @@AlphaSigmaGaming
Me from india
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 😂
@@anmolnarayan214 okay little minded hobgoblin
@@anmolnarayan214 yoo bro 💀💀💀
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 🤣🤣
Your handwriting is good
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.
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
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 🧡💥💫
Ans:(x²-5)(3x+1)
Meanwhile indians and South Koreans kids be like ..... Why he lifting pen for such an easy question
This is so helpful shorts.
When you know what’s 3x+1 really about
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
😊😊😊😊
😊
Thank you bhaiya ❤
Thanks dude 😎
Nice explanation sir🎉
Thanks!
Excellent
Nice handwriting ❤
We can also factor (x - _/5) into (_/x + 5^¼) (_/x - 5^¼). Should it be done? No.
Nice method dude
Keep it up
Nice 👍
Incredible🔥
Wow what a good explanation 😮
Grear explanation. This is a simple as it can get
Bro you made me understand this shit thanks bri
I had a mini heart attack when I heard "3x+1"
thankyousomuch! I was trying to solve question for hours and your this method just help me out thankyou
Thank you🙏💕❤
You can already see that this is one of the easier to factor 3rd degree polynomials
watching from Bangladesh 🇧🇩 ❤
Thanks a lot ❤
Can you also solve it by using Bézout's theorem?
sometimes this method is just confusing so better do synthetic division.
Thanks you have made my doubt a huge doubt
Best way
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 ❤
Bro just showed me how to solve my calculus problems in a simple manner without banging my head against the wall, I appreciate it🐧
Very very thanks. I was struggling in this problem but your solution gave me an idea about this. Thank you once again. 😊😊😊😊😊😊❤❤❤❤❤❤
X^3-8x^2+4x+48=0
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.
Thank you sir❤
- FROM INDIA
It's an amazing method to solve the problen
Thank you sir
To teach the method, you have to card stack by creating a workable polynomial before you turn the camera on. 😅
thanks i need this so much thanks
Nice
After 12 hours of work, six hours of derivative exercises in math... I can tell you that my brain is now broken lol
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
Amazing 👍
Maza a gyoo
It all went to shit when they introduced Alphabets to math...
Don't you need both terms in the binomial to have a square root non-involving decimals for it to be a perfect square?
thanks bro
🎉 good sir
Factoring by grouping method
not working 🙄
Lol, maths be like- u can't make fun of me
Bro wrote the best root sign
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
I am glad to find a very good explanation video 🤩🤩
Thanks!!!!
just use foil..
What if the last two parts diesnt even match up
(3x+1)(x^2-5)=(3x+1)(x-√5)(x+√5)
Please help me with matrix 2by 2
Hey man try to be patient
powlyNOOMyoooll
👌👍👍
Just use factor theorem
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.
thanks
Perfect
Where did the 3x∆3 go to
Math 😩❤️❤️
If it is a factor theorom?
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.
❤❤
I never learned to do that
it was very easy
Simple
3x÷ 1
😮
Factorization is one of the most easiest chapter ever
We are studying it in class 8th of India
This is basic 9th grade question.
Why do people make it more complicated than it has to be?
I don’t fully understand still 😢
I wanna kiss this guy that was helpful
You really need that √5?
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
Sir for me exam sir please say sir like that sum sir
99% Indian students 😂
why would be plus
You don't want to put these many steps here😂
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
😂😂😂😂😂😂😂