Factorising Harder Quadratics (Higher Only) | GCSE Maths Tutor

A video revising the techniques and strategies for factorising harder quadratics - Higher Only
This video is part of the Algebra module in GCSE maths, see my other videos below to continue with the series.
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🔹 Watch the video
🔹 Make notes
🔹 Practice the questions
🔹 Mark your work
🔹 Review what you have learnt on the exam questions
Part 1 - Laws of Indices - • Laws of Indices (Highe...
Part 2 - Collecting Like Terms - • Collecting Like Terms ...
Part 3 - Expanding and Simplifying - • Expanding Single Brack...
Part 4 - Double Brackets - • Expanding Double Brack...
Part 5 - Factorising - • Factorising (Higher & ...
Part 6 - Factorising Quadratics - • Factorising Quadratics...
Part 7 - Substitution - • Substitution (Higher &...
Part 8 - Changing the Subject Part 1 - • Changing the Subject o...
Part 9 - Simultaneous Equations - • Simultaneous Equations...
Part 10 - Changing the Subject Part 2 (Higher Only) - • Changing the Subject -...
Part 11 - Expanding Triple Brackets (Higher Only) - • Expanding Triple Brack...
Part 12 - Factorising Harder Quadratics (Higher Only) - • Factorising Harder Qua...
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[@Love.every.bit.of.life123]

Imagine entering this with an empty brain and finishing the video with the highest knowledge...I dont know how to thank you, I have a exam in a few days and I understand everything in Maths except this one and I struggled a lot. But now I can finally go in and finish my assessment with full confidence that a teacher here gave me. 👌

[@TahsinRahman-hl9zh]

Lol

[@TahsinRahman-hl9zh]

Did u do ur gcse this year How did it go bro?

[@Love.every.bit.of.life123]

@@TahsinRahman-hl9zh nah I'm doing it next year, finished year 9 tho. But this actually helped me do better in the maths test

[@Love.every.bit.of.life123]

@@TahsinRahman-hl9zh we start GCSE from year 10, but idk about other countries🫠

[@TahsinRahman-hl9zh]

@@Love.every.bit.of.life123 yooo bro same 💀

[@kkbossop7223]

This youtube channel is seriously the reason I topped in my exams. like so many of the questions he discussed in some of his videos came and I could solve them easily. Cant thank you enough bro. Every topic in my syllabus I'm learning from you. first I see the question and try to solve myself, if I am stuck then I continue your video, best way for practice.

[@to_discover_life]

exactly the same for me

[@sapna1387]

doing last min revision, have a mock in few hours, this is really helping. thankyouu sir

[@sapna1387]

@CompanyOwner ⤴️ okay so I got a grade 8, so happy with it, I was really expecting a 7 but then ig this really helped cuz he goes thru so many exam questions which are similar to the ones found in the exam papers.

[@Sophia-ok4ce]

@@sapna1387 yayy that’s so good well done :)

[@anwar4649]

Omggg mine is in 10 hours 😭😭

[@elise7407]

@@sapna1387 me right now

[@okay4567]

same lmao it’s 4am

[@JOSHHXX]

YOU ARE AN ABSOLUTE LEGEND! I DIDN'T UNDERSTAND WHAT YOU HAD TO DO WHEN THE COEFFICIENT WAS MORE THAN ONE AND YOU JUST EXPLAINED IT SO MUCH MORE COHERENTLY THAN MY TEACHERS TYSMMMMMMMM

[@TheGCSEMathsTutor]

So glad to hear the channel is working for you! Great news 😁🙏🏼

[@aqacquires4243]

agree

[@jbait9969]

Dont lie g

[@aife1398]

@@jbait9969 the guy aint lying dude, the guy is pretty helpful

[@Tcurrcrcrb]

really helpful ! I find quadratics hard usually but you have made it easier, thank you.

[@TheGCSEMathsTutor]

Amazing news! Always great to hear that the channel is helping so thank you for the kind words! 😁👌🏼👌🏼

[@jamesalster4304]

@@TheGCSEMathsTutor if i solved all of these questions via completing the square will i still get the marks or not?

[@alecanicecuppatea]

@@jamesalster4304 it depends on the question, it may say solve by factorising or solve by completing the square

[@lukethody5035]

The intro is so groovy, I wish all teachers at school started a lesson like that

[@kreemafham]

it gets annoying when its your 20th time or smthing

[@lukethody5035]

@@kreemafham lmao true... no way that's from a year ago that's wild

[@kreemafham]

@@lukethody5035 are you doing cambridge or edexcel? i have my maths paper 2 in 4 days :(

[@Sportcat01]

Thank you so much! My maths teacher gave me a sheet on these type of questions and first of all I got 2/20 and now I’ve watched this video I did the sheet again and I managed to get 19/20 thanks so much! Your explaining is top notch!!

[@TheGCSEMathsTutor]

Wow that’s some incredible progress right there! Well done for going out of your way to find this video and revise it in order to improve, I love it when hard work pays off and here it clearly did! Well done 😁 are there any other topics you’ve struggled on?

[@Sportcat01]

@@TheGCSEMathsTutor thank you sometimes yeah , the topic I’ve struggled most on is probably surds . I’ve watched your videos and it helped me understand it a bit better so thank you👍 just practise is the key for me and trying to attempt more questions . I’m in year 10 so plenty of time to attempt more kind of questions . Just a couple topics maybe I struggle on and could do with your spectacular help . Firstly , I have said this and you said you will try and make a video on it . It’s about like typical exam questions in higher paper when the involve fractions , and percentages and there usually like 4-5 marks . Another one is probably angles in a typical exam question . For example, a lot of maths test papers I’ve done particularly in higher, they are like 3 triangles joined together and they may say find x, y, z they are mostly kind of questions I’m stuck on. So perhaps can you do a video on that too? Also just one more question related to quadratics : for example simple quadratics like x^2 + x+ 2 - will they only appear on foundation paper?

[@TheGCSEMathsTutor]

@@Sportcat01 Aaaah great news! Surds is my favourite, I’m planning to make a few new videos on surds once I can! Definitely just keep practicing them! And yes I’ve got the fraction/percentages one on the list, I’ll have to see which angles questions you’ve been looking at, I’ve done some in parallel lines etc that may be helpful? The last one there sounds like factoring a quadratic, I’ve done a few on both expanding and factorising quadratics in the algebra playlist that appear on both exam tiers have you found them? 😁🤞🏼

[@Sportcat01]

@@TheGCSEMathsTutor thanks for the videos your going to do on the fraction/ percentages Yes one of them was for example in parallel lines and I’ve watched your tutorial too and it’s much more understandable but sometimes in the exam paper, it’s in a format and there are lots of lines and there is for example an area where I get stuck .also what I sometimes got confused on was if the angles are corresponding, alternate or interior . But sometimes they’re like joined together with no parallel lines and that’s when I get confused on

[@TheGCSEMathsTutor]

@@Sportcat01 you asked for fractions, percentages and ratio and here it is: kzbin.info/www/bejne/j3fGlGWgrZWSd5o 😁🙏🏼 really hope it helps!!

[@Nehselo]

I DID IT!!!!!! THIS WAS SO DIFFFICULT FOR ME BUT FINALLY I SOLVED QUESTIONS BY MYSELF THANKYOUUUUUUU SO MUCH YOU ARE THE REASON WHY I SUCCEED MAY GOD BLESS YOU YOU ARE THE BEST I SWEAR

[@magpiestudent9357]

It really pays to have good mental arithmetic when solving the more complicated quadratics quickly. Mine is lacking so it takes me ages. I'm hoping with increased practice I will improve and get quicker. Listing the factor pairs helps a lot.

[@sabihbehzad441]

I was struggling so much on these harder quadratic factorising but after watching this video I rally understand. thanks SO MUCH

[@sinaisafo5300]

sooooooo helpful i literally have on online test since this coronavirus thing got the uk on lockdown tomorrow and have just been looking for videos on utube

[@TheGCSEMathsTutor]

Sinai Safo Great to hear! Tonnes of videos in the playlists just let me know if there are any topics you are looking for 😁🙏🏼

[@sinaisafo5300]

@@TheGCSEMathsTutor oh my gosh thank you sooooooo much

[@TheGCSEMathsTutor]

Sinai Safo No problem at all! 😁🙏🏼

[@janestrachan]

you've LITERALLY saved my life. I can't thank you enough!

[@ItsMe-eu9br]

Thank you so much for your help! Just started revising for GCSEs 2021.

[@TheGCSEMathsTutor]

It’s Molly Amazing! Plenty of content on here to keep you going! 😁🙏🏼🙏🏼🙏🏼

[@itsluke6851]

Same here

[@ItsMe-eu9br]

@@itsluke6851 good luck!!

[@Unknown-wp8pu]

same here bro. Good luck

[@ItsMe-eu9br]

@@Unknown-wp8pu same to you!!

[@carolynmitra8837]

For the last question (9x -15) (x+1) works too

[@marxcarton3858]

no, it doesn't factorize fully so, it would be 3(3x-5)(x+1)

[@anonymous99923]

@@marxcarton3858 well his answer of (3x+3) also isn't factorised fully

[@ha1der06]

im not understanding why one will double and the other will triple?Can anyone help 9:25

[@ram1588]

6=3X2

[@claireshoniwa5801]

This video really helped my disabled classmate Jordan we are forever thankful

[@Khaldoon.Arshad10]

Love ur videos. Thank u sooo much. Helped me since i started secondary now im in yr 10!!!!!🥇🥇😀😀😀♥️♥️

[@TheGCSEMathsTutor]

So glad to hear it! Can’t wait to hear how you progress with another year, good on you for starting early! 👏🏼👏🏼

[@fourspinners6981]

Love the video ! in fact you havent made one bad video that i have seen. Did a maths test today and without you wouldnt have done well , so thank you very much !

[@rogueart9100]

i couldn’t understand any of this when it was taught and i just completely learned it from you in 15 minutes , fair play

[@tenshikaede]

Literally your explaining skills are beyond amazing

[@AJ-hj8bb]

Thank you for this! I've finally found a method i actually understand :D

[@officialfallguystips6825]

Hey sir these are amazing videos they are really helping me with the higher paper I was thinking can you do a video on vectors.

[@TheGCSEMathsTutor]

Florjan Toro Thanks for the feedback I’m glad they are helping! I will add vectors to my list for you, I’ll post the link here once it’s done! 👍🏼

[@officialfallguystips6825]

@@TheGCSEMathsTutor thanks a lot

[@officialfallguystips6825]

Oh and sir if you don't mind can you make a video on algebraic proof hard ones

[@TheGCSEMathsTutor]

Florjan Toro Another one added to the list 👍🏼

[@officialfallguystips6825]

thank you

[@studyaccount7451]

i love your videos and have watched almost oall of them because they're that great but please lower the volume for your intro 🥲😭😭

[@Mislam-ql2bz]

thank you so much you explained it better than my teacher

[@nasradaoud9383]

I’ve been bing watching GCSE maths tutor very nice, is there an algebraic fractions part 2 since there is a part 1?

[@StudyWithTeaAddict]

For the last question, wouldnt (9x - 15)(x + 1) also work? Can you have multiple versions of factorising something and all of them be right?

[@gabbyidk5428]

that's what I was thinking, I got the same

[@yemon]

thank you so much, my finals are tomorrow, and I am trying to learn everything before it. thank you so much

[@TheGCSEMathsTutor]

Amazing news! I’m so glad to hear the channel is helping 😁🙏🏼

[@quinamasarira2116]

thank u. you are going to help me pass, the 2021 may/june IGCSE exam.

[@camzyboxedyou6870]

Should you do this or the grouping method ?

[@amaan1549]

Can you put the marks alongside questions so we can get a rough idea of how much time to spend on the question in an exam situation?

[@TheGCSEMathsTutor]

I’ve completed the GSCE curriculum now but my revision guide coming soon should be helpful for that 😁🙏🏼

[@Joe_auto]

thank you so much i tried so many sites dr frost senca nothing i almost gave up till u just made me a 10/10 on this topic i find it very very easy now tysm

[@Scary_Momo]

This video gave me an extra braincell.

[@balsammohammed9140]

hello quick question, would (x+2) (2x+6) be incorrect for the first question that we got to do, because when i expanded the brackets i got 2x^2+11x+12

[@sinaisafo5300]

can u do one on loci and bearings pls

[@TheGCSEMathsTutor]

Sinai Safo Bearings here - kzbin.info/www/bejne/iH6nnWmwotqGfJI but Loci is going to be a bit delayed as I need to do this using a camera and still working out the best way and getting to a shop to buy equipment is not an option at the moment 😥🙏🏼

[@SP-sq6rr]

For the question at 10:44, I did it a different way and got (6x + 6) (x + 2). Is it still correct?

[@TheGCSEMathsTutor]

There are often two ways to factorise these harder quadratics, expand it out and see if it matches, always the best way to check 😁🙏🏼

[@SP-sq6rr]

@@TheGCSEMathsTutor thank you

[@klaidi9294]

what if you factorise different but still get the same answer when you expand would you still get the mark for the answer?

[@wiamel-f7d]

ive seen other people use another method. is this method easier ??

[@qui-wan1977]

Thankyou so much! Your videos have been soooo useful :)

[@user-fy5yf2jt3n]

Hi is there a spefic method for factorising quadratics with x squared, y squared, and xy

[@yooheyy9934]

excuse me but how can i differentiate whether it is a factorising quadratic question and a harder factorising factor though because both types of questions look the same

[@Humnaliii]

for the last question does it matter which way round i wrote the numbers ?

[@Anime_World1168]

this man i saving my life

[@tsTURTLE]

in 9:04 what if we use the other pair( 6x )(x )? will that also be alright?

[@fozyleen9737]

Thank you so much for this !

[@erenyeager6668]

i fully appreciate it sir

[@arbab_03]

Life saver!❤️❤️

[@carlosdano849]

Does it matter which way u put the numbers. For example can it be (3x-3) (3x+5) (3x+5) (3x-3)

[@teamsupers9046]

Yeah

[@ZZZ-le6xd]

it doesn’t matter

[@ausa0717]

this was rlly helpful thanks

[@Legend34343__]

Can someone explain the steps to this problem: x^2+10x-24=0, solve for x, please help

[@b07x]

You have to use *Completing the Square* method for that. x²+10x-24=0 You half the *b* (which is 10, 10÷2=5) and you put it in the following format (x+5)² then take away (b/2)² (5²=25). so (x+5)²-25 then add the *c* So (x+5)²-25-24=0 (x+5)²-49=0 (x+5)²=49 x+5=(49)½ (Square rooted both sides) x+5=7 x=7-5=2 Now check it (2)²+10(2)-24=4+20-24=24-24=0 Solved 🙂 x=2

[@efaclip5938]

Super helpful! Tysm

[@moonboo3mwah193]

THANK YOUUUUUU AHHHH!!!!

[@TheGCSEMathsTutor]

My pleasure 😁🙏🏼

[@esosaae9296]

THANK YOUUU SO MUUUUCH

[@marxcarton3858]

at (13:54) couldn't the answer also have been 3(3x-5)(x+1)

[@sandramoh1763]

thanks so so much!!

[@abdikaadirnasir]

Thanks❤

[@HaZecLaN-eu]

10:48 was wrong, you didn’t swap the numbers

[@darnellbailey5038]

thank youu👌🏾

[@jasopyuh]

Please come up aswell

[@choco1026]

thx dude :)

[@moisheschleider6189]

thanks so much you really helped me understand this topic

[@jasiien]

I LOVE YOU SM OMG THANK YOU I WILL ALWAYS BE UR FAN U HELPED ME SM🫶🫶🫶

[@youssefhili3410]

Thxxx

[@kronomcs]

I learn this in year 7 is that normal?

[@fifimazing4458]

what school do you go to?

[@Toneri_Inu]

​@@fifimazing4458military school

[@louismarshall176]

55 mins til exam

[@TheGCSEMathsTutor]

Good luck 🤞🏼🤞🏼🤞🏼

[@magpiestudent9357]

How did it go?

[@amakangadi8780]

Madness

[@gwpoooo]

hello

[@SaqPK]

Bruv ur waffling this 1

[@mohamedessamtawfik182]

.

[@mohamedessamtawfik182]

..

[@skykingtenz1232]

Why didn’t you tell times two by town in the first question

[@skykingtenz1232]

2 times 2

[@lenasada251]

تسهاسيتهه

[@lenasada251]

OOOOOF

[@hugooliver3835]

Is it just me who thinks that intro music is banging

[@TheGCSEMathsTutor]

Haha glad to hear it 🤣👏🏼👏🏼

[@hugooliver3835]

@@TheGCSEMathsTutor what music is it?

[@TheGCSEMathsTutor]

@@hugooliver3835 It’s linked in the bottom of the description, commenting back on YT studio so not sure which one is on this video 😁🙏🏼

[@bluelite7205]

@@hugooliver3835 yeah its good

[@magpiestudent9357]

I find it amusing that you have this really loud intro music and when it stops this gentleman has a calm and measured voice.

[@lenasada251]

Aaaaaaaah

[@neonbiock730]

I dont really understand this method, the one my brother taught me is better.

[@bjt8764]

Hate to be pedantic, but... ;-) You never did the last quadratic correctly. (i.e. 9x^2 - 6x -15). The correct answer is (3x-5)(x+1). The reason is: 9x^2-6x-15 simplifies to 3x^2-2x-5. Hey, but very helpful :)

[@TheGCSEMathsTutor]

Jabberwocky-123 Unfortunatey that isn’t correct, you can only simplify a quadratic down when it is an equation, for example if it was equal to zero. When factorising an expression you can’t simplify it first! 😁👍🏼👍🏼

[@bjt8764]

@@TheGCSEMathsTutor You're trying to wriggle out of this one. Why are you factorising this quadratic? To find the roots! That's the whole point, to solve the equation. And finding these factors is premised on the equation equalling zero. When we say (x+1)(x+2), that's telling us where curve crosses the x axis where y=0. Other than as a practice exercise, factorising expressions is pointless.

[@TheGCSEMathsTutor]

Jabberwocky-123 This isn’t solving quadratic equations so no, we are not trying to find the roots, however if you would like to practice this topic then I can send you the video link. This video is focussed on factoring a quadratic expression which is part of the GCSE curriculum and a stand alone question that appears on exams, we use these not just for solving to find the roots but also in other topics such as simplifying an algebraic fraction involving a quadratic. The method you referred to is incorrect and would result in no marks in an exam so it’s very important that students understand the difference between manipulating an expression and when to use it as opposed to solving a quadratic equation and when to use that 😁👍🏼

[@lailataluminousnight8064]

@@TheGCSEMathsTutor you are cool😏

[@Toneri_Inu]

This comment section is confusing me pls help

[@yasminx5845]

who has the audacity to dislike a video of someone so kind just spreading his knowledge and helping others bruh

[@kreemafham]

they the ones who failed

[@muhammad984]

why do i have to go to maths class when i can learn from this guy?

[@noannboussac7551]

you are carrying my revision!

[@redoract5534]

honestly everything I don't understand, you make it look like 2+2

[@TheGCSEMathsTutor]

I’m so glad to hear that! Always great to hear the channel is working for you! 😁👌🏼

[@amadif1793]

Thank you for making these topics easy to understand 👍

[@omz2683]

Thanks man very useful keep it up👏

[@TheGCSEMathsTutor]

Thank you! I will do 😁🙏🏼

[@mqry_ii]

whos here for tmrws paper 2

[@Hadia-xj4ni]

Why couldn’t you pick 1 and 4 and have to pick 1 and 2 someone please explain I’m very confused

[@TahsinRahman-hl9zh]

Also u can also factor these by grouping

[@shabadkaur6465]

Awesomely Flawless explaination

[@TheGCSEMathsTutor]

Love that 😁🙏🏼🙏🏼

[@shabadkaur6465]

@@TheGCSEMathsTutor Sir I have a few doubts. Plz let me know when available

[@MrGodlyBacon36]

much love bro helped out so much for revision!

[@TheGCSEMathsTutor]

So glad to hear that 😁🙏🏼

[@tess6484]

hello sir shouldnt the last one be (9x-15)(x+1)?

[@kjjk451]

11:30

[@mohamedessamtawfik182]

...

[@tk.3185]

Say for example the question at 12:58 How do you know whether to use (6x )(x ) Or (2x )(3x )

[@enta3325]

im here from the simultaneous equation video loll i was so lost with the (5x+4)(x-2) thing

[@ZaynChowdhury]

4:20

[@mc45892]

hi how do you know which number to put in the brackets when you have found the factors

[@Anolahmusic]

Ur videos have been super duper helpful so far but I am so confused about the 2x^2-9x+10 because You doubled the 2 =-4 which was paired with - 5 but that doesn't multiply to positive 10?? Sorry lol its probably a really easy mistake but I was boggled

[@alisha3771]

the final answer is (2x-5)(x-2) because you have to go back to the original factors of 10. there is a -2 instead of a -4 because that will eventually get multiplied with 2x to get 4x. if you expand it out, you get positive 10 as -5 times -2 = 10.

[@kyzah9123]

Thanks this really helped

[@khadijamuntaha8252]

thanks so much, school right now is really stressful so great vid!

[@noahbackson2613]

nah bro you genuinely helped me so much

[@michaelrosenke1167]

someone tell this man about the magic X

[@pacifique6725]

Guy is an absolute legend.