check out various values of x which satisfy the equation. x=2 is a solution so x-2 is a factor. Now divide x^3-x-6 by x-2 to get the quadratic factor and then solve the quadratic factor in the normal way.
There are many other ways. Graphical methods, where the graph crosses the x-axis (computer software could do this) or use iterative methods (C3 module) or Newton Raphson method (Further maths). Just some of the possible methods.
You must remember that not all cubic equations factorise, just like with quadratics. If there were decimal coefficients then I would multiply through by some value to make them all integers. So if it doesn't factorise there are other methods to use like iteration, Newton Raphson methods. Check this out on my website under numerical methods.
Oh my! Thank you very much, my big exam (O level add maths) is in two weeks and I always had problems with this , but not anymore, thank u very much 👌👏
Please chance the title because it's a cheat. You dont show how to solve cubic equations becausr you "try" to find solutions empirically. You just solved this "ready made" equation that is fiactorizable, and has a rational solution of -2. You didn't show how to solve any generical cubic equation. To "solve" means to find polynomial zeroes, and you just said to "try divisors of the known term", but "trying" cannot work with a class of infinite numbers.
the generic way is to use the factor and obtain a root, and with that root u use synthetic division(extremely easy) to get a depressed eq will a quadratic eq. u can then simply solve that quadratic eq and hence get the 3 roots (1 from factor theorem and 2 from depressed quadratic eq). u can even solve equations of higher degree easily using this method
thx a lot man i have my additional mathematics o levels tomorrow and was stuck at this cubic stuff awesome way to solve it. the long/short division is a pest!! cheers
Then if you are solving (x-2) (x^2+2x-6)=0 then just use the quadratic formula to solve x^2+2x-6=0. If it is not an equation then you just leave it at this stage.
Thank you so so much for this video!! I'm finding maths really hard at the moment and this will make it much easier... beats squinting at my teacher's squiggles on the board!
Very nice, but could you explain why I have to look at the constant term factors. What is the reason that I analyze it? Where does the "trick" come from?
For those who are unaware, there is a calculator trick that you can use to find the solution automatically to cubic or quadratic equation. If you are in possession of a Casio fx-991es plus, just press on, .mode 5, 4 then you input the equation into the calculator and it solves it. This type of calculator is not a graphing or programmable calculator therefore it can be legally used in tests.
Literally have my exam in 40 minutes and im watching last minute videos because I didn't revise.. thank you! Your video is still helping people 12 years later Lol
I've been trying to teach myself maths to prepare for university entry, and you sir have just made my WEEK. I mean this strongly. I've been stuck on a cubic factoring problem for about six days now!
please can you tell me what will be the steps if the equation is x^3 + 5x^2 + 8x + 6 = 0 ? x+3 is a factor. how to solve the quadratic factor of x^2 + 2x + 2 ?
why not separate it into 2 binomials? like: (2x^3-5x^2)(-23x-10) because my teacher taught us that and Im not opposing your method just wondering how to solve it that way, please respond! thank you
thank you so much for these, just one small issue - are you sure it's (2x + 1) and (x - 5)? because i've worked this out and i think your signs might be wrong..if they're not, i am terrified because factorising is the least of my problems
Thanks a lot mate! Got an exam tomorrow and I've just been watching your videos all day. They are massive help! My teacher doesn't explain like the way you do at all. Thanks to you I actually get this stuff :D I hope I do well tomorrow!
Saving humanity one view at a time since 2010
Nice to hear that I am reaching the States. Greetings from the UK
Good to hear that you have made progress.
Excellent - Well done.
check out various values of x which satisfy the equation. x=2 is a solution so x-2 is a factor. Now divide x^3-x-6 by x-2 to get the quadratic factor and then solve the quadratic factor in the normal way.
Thanks from Watford,UK
Good to hear, thanks
There are many other ways. Graphical methods, where the graph crosses the x-axis (computer software could do this) or use iterative methods (C3 module) or Newton Raphson method (Further maths). Just some of the possible methods.
ExamSolutions to solve cubic equations I prefer to solve it visually using a geometry method found by an Australian engineer
You must remember that not all cubic equations factorise, just like with quadratics. If there were decimal coefficients then I would multiply through by some value to make them all integers. So if it doesn't factorise there are other methods to use like iteration, Newton Raphson methods. Check this out on my website under numerical methods.
@kclal cheers mate
Thank you and good luck. I hope I can continue to offer some help.
Oh my! Thank you very much, my big exam (O level add maths) is in two weeks and I always had problems with this , but not anymore, thank u very much 👌👏
Nice one!
Hope you did. Let us know.
Thanks this helped alot
Pleased to hear. Best wishes.
Thanks
Praise the lord i finally know how to do this ,helped me for my mathematical induction review ! thanks alot sir ! :D
Jemz Cerbito That's good.
Wouldn't I just love to be there at the moment. Weather terrible here in the UK. Anyway, greetings from the UK.
Greetings from the UK
Great video!!! Excellent teaching and a good trick too.It really has helped me a lot.Best of luck.
Thank you!!!
No problem, pleased it helped. Best wishes.
Please chance the title because it's a cheat. You dont show how to solve cubic equations becausr you "try" to find solutions empirically. You just solved this "ready made" equation that is fiactorizable, and has a rational solution of -2. You didn't show how to solve any generical cubic equation. To "solve" means to find polynomial zeroes, and you just said to "try divisors of the known term", but "trying" cannot work with a class of infinite numbers.
yeah, but the cubic equation is pretty long
ZanteF12R you can use Newton-raphson to find the roots
got some works?
the generic way is to use the factor and obtain a root, and with that root u use synthetic division(extremely easy) to get a depressed eq will a quadratic eq. u can then simply solve that quadratic eq and hence get the 3 roots (1 from factor theorem and 2 from depressed quadratic eq). u can even solve equations of higher degree easily using this method
dont get onto the main man
You could draw a graph and see where it crosses the x-axis
Everyone would :)..weather here is sunny but can get a little rainy..awesome vids man.
thx a lot man
i have my additional mathematics o levels tomorrow and was stuck at this cubic stuff
awesome way to solve it. the long/short division is a pest!!
cheers
@ThePrinceDaniels No probs.
That's good.
@kikhalili No probs
Just want you to know ExamSolutions .I wrote A levels last year and thanks to you I went from C to A in 2 months. Le boss!!
Well done. Would appreciate it though if you could say this on the page ruclips.net/user/ExamSolutionsdiscussion if you would. All the best.
OK. I can't find where to type it but when I do I'll put the text there
Thank you very much Sir, this is way more easier than the method taught at the University
Thank you! This helped
Good.
this is very very useful compared to the teacher in my university thank you very much
Great. Very helpful lesson. Well explained.
easier way: after u find the factor.use it to divide the factor. After that u will get a quadratic function which is able to factorie.
Where?
Wow I can't believe I didn't know this method already! Thanks from California!
Then if you are solving (x-2) (x^2+2x-6)=0 then just use the quadratic formula to solve x^2+2x-6=0. If it is not an equation then you just leave it at this stage.
Great video man, I was pretty rusty on the subject and I immediately got it again. Cheers! :)
wow thank god i found this!!!! this is just awsome !! Good job :)
Thank you so so much for this video!! I'm finding maths really hard at the moment and this will make it much easier... beats squinting at my teacher's squiggles on the board!
thanks, this really cleared thing for me.
From U.S.
i always used the synthetic division to find the other factor, never looked at it that way... cool. thanx
simple and efficient explanation.
Thanks! This helped a lot!
Very usefull, thank you sir!
Omg dude! Thank u. I just understand now, lol. Though Im nearly having my big exam which is O level. Im from Brunei and Thank u so much, again! (:
Hope it goes well for you. All the best from the UK.
Very nicely explained.
You can also use Horner scheme to find the ax²+bx+c instead of trying to figure them out.
no one wants horny scheme u doofus stop yappin
thanks a lot for this video it was very helpful......
Thanks from Trinidad (Caribbean)
further maths exam tomorrow, this may have saved my life. Thank you kind sir!
Sizz Fizz Wishing you every success.
@EMaster9 Then it is unlikely to factorise.
this is soooo helpful!!! thanks!!!
You're welcome
gosh i love so much for helping me out with this one .
Thank you very much!
Aye, watched you guys play a couple of times!
very nice teaching and concept clearity,thnku sir god bless u
And you.
well done sir! You saved my life! Round of applause!
Pleased to hear that I may have stopped that crying then. Good luck for Wednesday.
Found this very helpful thanks alot
OOHH your are awesome seriously! God bless you man :-)
Thank you very much, very helpfull
Very well explained
Thanks from Milton Keynes!
What if you cant guess the number to set it to 0?
is there a way to work it out?
No
i think I didn't fully understand my teachers method, I had a test on it today and I think I aced it because of you!
thx for ur tutorial, it's very clear and helps a lot!!!
You're very welcome.
Pleasure
Thank you very much ❤❤
I'm wondering as well. For starters your expression does not expand to give the expression in the video. I think there is confusion with your method.
thank you so much!!!
it was an A!
didn't miss one thanks!!!
Very nice, but could you explain why I have to look at the constant term factors. What is the reason that I analyze it? Where does the "trick" come from?
For those who are unaware, there is a calculator trick that you can use to find the solution automatically to cubic or quadratic equation. If you are in possession of a Casio fx-991es plus, just press on, .mode 5, 4 then you input the equation into the calculator and it solves it. This type of calculator is not a graphing or programmable calculator therefore it can be legally used in tests.
Thank you soooo much....that really helped a lot :)
Literally have my exam in 40 minutes and im watching last minute videos because I didn't revise.. thank you! Your video is still helping people 12 years later Lol
thank you that helped alot it was a much better explanation than my teacher gave me
😍😍 thanks a lot ....
Pleased to have been of some help.
Tomorrow is my maths test .and hell yeah ..i got in the right place =)
you should use the formula
(-b +- √b^2-4ac)/2a
in your case
a=1 b=2 c=2
Replace in the equation, it should be in decimal and you will get your answer
@pinkfloydfreaks1 from one pink floyd lover to another - hope it goes well for you.
@TheMerovingion Don't know if that's a good thing or not?
great vid bro
I've been trying to teach myself maths to prepare for university entry, and you sir have just made my WEEK. I mean this strongly. I've been stuck on a cubic factoring problem for about six days now!
Thanx.. Perfect.. :)
ty i almost forgot the FACTORS THEOREM FOR MY TEST TOMORROW!
Epic i couldent find a gokd vid but this is helpfulll
please can you tell me what will be the steps if the equation is x^3 + 5x^2 + 8x + 6 = 0 ?
x+3 is a factor. how to solve the quadratic factor of x^2 + 2x + 2 ?
It was '=0' so would the answer be x= (-1+√7) or (-1-√7) or 2?
Thanks, your videos are hugely helpful.
thanks a bunch pal
sir u are awsome thankyou
Thank you, thank you, thank you, thank you, thank you!!!!!!!!!!!!
+Science Rocks That's okay. Thanks for using.
why not separate it into 2 binomials?
like: (2x^3-5x^2)(-23x-10) because my teacher taught us that and Im not opposing your method just wondering how to solve it that way, please respond! thank you
Oh my god
Thank you so much...
This was so helpful, your so awesome
thank you so much for these, just one small issue - are you sure it's (2x + 1) and (x - 5)? because i've worked this out and i think your signs might be wrong..if they're not, i am terrified because factorising is the least of my problems
8 years later, yes they're correct
Thanks much sir! These videos are very helpful beyond A levels. I used your Statistics tutorials as well. Great work!
what if the constant at the end is, A. how do i put that into the linear factorising part?
@Zyphr456 Good Luck - Hope all goes well.
Thanks a lot and keep up the good work. You helped me a lot in my Calculus subjects!
Thanks a lot for the video, I always feel like lecturers mess this up when they teach. I'll always remember it now.
Good
Thanks a lot mate! Got an exam tomorrow and I've just been watching your videos all day. They are massive help! My teacher doesn't explain like the way you do at all. Thanks to you I actually get this stuff :D I hope I do well tomorrow!
How was the exam?