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Step by step Factorise :

Please show me the steps for how you would factorize this.

3x^2 - 22x + 7

Thank you !
Hi!

I think the easiest method here is using a calculator, but obviously you want all the steps so I'll just go through them quickly.

We know that to get to 3x^2 we need 3x and x together so now we already have half of our factorisation done -- (3x + n) (x+p)

Now we need to find n and p

For the -22x we can get through our previous knowledge, which is the fact that there is a 3x somewhere in there, AND another x in there as well, so we can just do 3 * -7 which equals -21 and then for the other x we can do it x * -1 which is -x -- just add those together and they equal -22x.

Usually for the second thing (usually with x) in the equation its always addition of the two different variations (not sure if i'm explaining this right)

After it, the third thing in the equation is ALWAYS multiplication, so since we already have -1 and -7 we can easily just multiply those together and get +7

What the main thing to realise here is that the two variations that you have found fit into BOTH the addition and the multiplication processes, so even if you found something in the first addition thing that added up to -22 but didnt multiply together to make +7, then it's WRONG! My method is probably really wrong but it's the only way I can really do it, I'm sorry if it isn't that helpful lol

which overall gives us the information we need;

(3x-1) (x-7) is the answer -- in case ur confused which one is n and which one is p, just remember that 3x HAS to be multiplied by -7 so it cannot be in the same bracket.

I'm really sorry if this explanation was all over the place lol.
(edited 4 years ago)
Omg, completely forgot about one of the easiest methods I know out there that I use ALL the time.

The quadratic equation!

x = -b plus or minus the square root of (b^2-4ac) all over 2a

So here the a = 3 and b = -22 and c = 7

Just put those into the equation, but you'll get the OPPOSITE of what you want.

So for the first one you'll get 7 so that means you have to enter (x-7) and not PLUS, just switch it around.

Now for the second one its a bit more tricky, the answer will show up as 1/3 and you just need to take the 3 from the bottom to use it as the coefficient and then the 1 on the top, you switch to negative

In the end, it'll be (3x-1) which is what we got in the earlier method I mentioned above.

Hope these two methods helped u in sum way xx good luck to you! What year u in?
Original post by jade_oswell_89
Omg, completely forgot about one of the easiest methods I know out there that I use ALL the time.

The quadratic equation!

x = -b plus or minus the square root of (b^2-4ac) all over 2a

So here the a = 3 and b = -22 and c = 7

Just put those into the equation, but you'll get the OPPOSITE of what you want.

So for the first one you'll get 7 so that means you have to enter (x-7) and not PLUS, just switch it around.

Now for the second one its a bit more tricky, the answer will show up as 1/3 and you just need to take the 3 from the bottom to use it as the coefficient and then the 1 on the top, you switch to negative

In the end, it'll be (3x-1) which is what we got in the earlier method I mentioned above.

Hope these two methods helped u in sum way xx good luck to you! What year u in?


Thankyou so much!! This was so helpful!!!!

I'm in year 10 :smile:
No problem! I'm also in Year 10, but taking my GCSEs this year, it SUCKS!
Original post by SmartUnicorn
Thankyou so much!! This was so helpful!!!!

I'm in year 10 :smile:
Original post by jade_oswell_89
No problem! I'm also in Year 10, but taking my GCSEs this year, it SUCKS!


How come you aren't taking them next year? 😬 and yeah it does
Our school likes to do that, I'm not sure why, but you start learning the GCSE syllabus from Year 9 on to Year 10, where you do ur exams at the end of Year 10. Then you take A-Levels from Year 11-12, and then that's it, you're outta there.
Original post by SmartUnicorn
How come you aren't taking them next year? 😬 and yeah it does
Original post by jade_oswell_89
Our school likes to do that, I'm not sure why, but you start learning the GCSE syllabus from Year 9 on to Year 10, where you do ur exams at the end of Year 10. Then you take A-Levels from Year 11-12, and then that's it, you're outta there.


Wow! how do you take in so much information (since you have one less year to learn) do you revise a lot? :smile:
Original post by jade_oswell_89
No problem! I'm also in Year 10, but taking my GCSEs this year, it SUCKS!


Why? Universities don't like early entry ...
I can't control it, it's how my school system goes. Honestly, if I could I would, but as of now I'm just happy I'm getting over with them.
Original post by Muttley79
Why? Universities don't like early entry ...
Original post by jade_oswell_89
I can't control it, it's how my school system goes. Honestly, if I could I would, but as of now I'm just happy I'm getting over with them.


Your parents can refuse to allow you to do it early - it may damage your chances of getting into a good uni!
Nope actually my parents can't. But Universities don't mind it at all, several of my older friends have gotten into Oxford and Cambridge (not saying I'll turn out anything like them) but it doesn't affect what Uni you get into.
Original post by Muttley79
Your parents can refuse to allow you to do it early - it may damage your chances of getting into a good uni!
Yeah, I do have to revise A LOT. They give us loads of tests and as of now, I am revising around 5-6 hours a day, which is taking a HUGE toll on me since I also have art coursework. Ew!

Original post by SmartUnicorn
Wow! how do you take in so much information (since you have one less year to learn) do you revise a lot? :smile:
Sorry you are wrong - your parents can refuse - I'm a teacher and you need parents to agree to early entry.

Things have changed recently and most schools have now stopped early entry ... it was different 5 years ago, even two years ago.
Trust me, my parents have tried countlessly. Either way, they're already scheduled and I've already gotten my statement of entry so it's a bit late now lol.
Original post by Muttley79
Sorry you are wrong - your parents can refuse - I'm a teacher and you need parents to agree to early entry.

Things have changed recently and most schools have now stopped early entry ... it was different 5 years ago, even two years ago.
Original post by jade_oswell_89
Yeah, I do have to revise A LOT. They give us loads of tests and as of now, I am revising around 5-6 hours a day, which is taking a HUGE toll on me since I also have art coursework. Ew!



WOW!!! I also have art coursework but how do you have 6 hours in a day to revise? after I get home I only have 3 hours until I have to go to sleep. Good luck though!! :smile:
Thank you! Well on good days i can revise up to 6 hours, but my average is around 4. I come back home at 4 and spend an hour having lunch. From 5 all the way to 11pm I study. However, if I have any afterschool activities then it's only for 3 or four hours. I like sleeping and working late so sometimes I stay up until 1am studying lol
Original post by SmartUnicorn
WOW!!! I also have art coursework but how do you have 6 hours in a day to revise? after I get home I only have 3 hours until I have to go to sleep. Good luck though!! :smile:
Original post by jade_oswell_89
Thank you! Well on good days i can revise up to 6 hours, but my average is around 4. I come back home at 4 and spend an hour having lunch. From 5 all the way to 11pm I study. However, if I have any afterschool activities then it's only for 3 or four hours. I like sleeping and working late so sometimes I stay up until 1am studying lol


Oh that makes more sense, I get home at 5 and also spend an hour and a half to get changed, eat and relax. Then I study until 10, but this is only on my mock week (this week) Normally I don't revise or if I do it's only for a few hours. I hope that offer my mocks I will study at least 3 hours a day after school and on Saturdays at least 6 hours. Sunday's to relax :smile:.

I wish I had that much dedication!!

Good luck! :smile:

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