And peeps, 1:10:00, in order to pass calculus, you need to have this factoring stuff down (I know from my own bad experience. Don't sign up for calculus until you have this stuff mastered, seriously). And 1:15:00 is some of the best math studying advice I've ever heard from any instructor, teacher, professor, whatever in my education career; he's dead right. 1:30:00 is factoring by grouping; this is the main method of factoring employed in calculus classes when trying to solve for limits, just a heads up.
This professor is an excellent teacher. I find myself not attending my own class. Instead I listen to his lectures, follow his examples, and low and behold, I GET IT! Thank God for Professors like Professor Leonar. I wish he was a professor at my school!
@Albi Marku I see, I thought intermediate algebra started in chapter 1. Have you found any good textbook or online worksheets to practices the content he teaches?
everyone says such nice things and i will not be different! Sir your patience when teaching is commendable! i am not a math guy and am going back to school for business after 15 years, your videos are actually making me enjoy math. i can't thank you enough!.
Hats off to you sir, I swear to God if you were my professor I would love Math and be waiting for the next class. Unfortunately, it's the opposite and the one I have is old and doesn't explain a lot, especially for those who graduated high school in different countries and go study abroad like me. I'M SO HAAAAAAPY THAT I FOUND YOUR CHANNEL.
I just want to thank you for your videos! Your videos are well explained and I know your students are fortunate to have you as a teacher. After watching your videos, I was able to ace the Accuplacer. After taking that test, I felt so proud of myself because my time spent watching your videos was rewarded. Keep doing what you do and trust me, you helping a lot of people out there including me.
Professor Leonard is truly an amazing teacher, his teaching methods is what I wish all my professors could do. He explains everything really thoroughly to make you better understand! And you can tell he loves his job and cares for his student, on top of that, he's definitely a looker! His wife is really lucky! But thank you for all that you do and putting the time to upload your videos, I feel like I'm a part of this class from where it's definitely helping me with my online class.
Professor Leonard,THANK YOU SSSOOOOOOOOO MUCH!!!!!! You are a true life saver! I am currently enrolled in MAT/117 at UOP and you are thee main reason why am going to pass this class. Thank gods that I found your youtube page from a google search. You make learning math exciting. Thank you for turning on the lights for me. Because before I was in the dark. Thank you for the clarity.
48:00 is also really a very important and subtle point. Since we distribute to get 6x+14, we don't include a variable in our GCF because 3x+7 is supposed to be thought of as a number, not a variable. It's written as 3x+7 because we are assuming this number is any number in existence plus seven. However, it's still one number, and multiplying it by 2 doesn't change that. So the question becomes, how do you multiply when you don't know the number before you multiply? The answer is distribution. This is the whole point of distributing. The whole point of factoring is to figure out what two numbers were multiplied together if all you can see is the finished product of multiplying. So, 2(3x+7) = 6x+14. In this case the result of multiplication is 6x+14. If we ask ourselves what was multiplied together to give 6x+14, the answer is 2(3x+7). Notice that 2 is the GCF of 6x+14. The whole point of finding the GCF is to be able to figure out what two numbers were multiplied together. As you might have guessed, 2(3x+7) is 6x+14 factored. And that's the whole point of factoring, and exactly how and why it works the way it does.
So, I started watching another one of his videos while doing my homework (haven't been in math in nearly 10 yrs, now taking stats.) Kept the video playing because I enjoyed the way he explained things. Even if I already knew it!
So i was supposed to take intermediate algebra at my college, and the class is too expensive, i thought it woukd be best to get a free book, and learn myself from different professors on youtube. Im so happy that i found this professor! He explains things so well, and to where i would understand! I already know some of these things, but it is a huge refresher!
I was really dumb at maths.. Didn't know how to even divide something properly but thanks to Mr Leonard.. I'm quite comfortable now in maths.. God bless you professor
@Professor Leonard I know this is old content and I hope you get a chance to read this.. but this has helped me greatly! I am 25 years old and I haven't been in school for so long and math was my worst subject!! You broke this down so beautifully I am going to college to become a game developer in a few months and I commend you for creating this amazing youtube channel and I am starting to find some love for math and the magic it brings to this world math is so miss understood and how important it is to us. I thank you Leonard I am very appreciative of you and your amazing work.
I love your style of teaching! You teach where I’m actually LEARNING & questioning why this is that or this to make it make sense! I’m thankful to have found your channel.
re-constructing my math skills again from going back to basics. I admit,my strong point is science but I'm not ashamed to be a beginner on mathematics. Hopefully after a year,I'll be good on my diff calc.
Going over Pr Leonard's playlists again, this time focusing on arithmetic, number theory and patterns to solidify my foundation of Discrete Math. Passed the Calculus track (Pre-Calc, Calc I, Calc II), and Linear Algebra, but Discrete Math kicked my butt. Simply couldn't do proofs, because I had lost my affinity with basic numbers and the WHY of doing certain calculations _this_ or _that_ way. Hopefully going this far back in times (even relearning simple addition and multiplication) is going to help me
I know this is probably an old video, but he reminds me of my Beginning Algebra instructor that I had Spring Semester 2022. He's on point like my instructor and made it easy for me to understand!
Mr. Leonard has a very interactive way of explaining the concepts and makes so fun to listen, man I also wish he was a teacher at my school. Thank you for what you do.
I literally love his way of teaching never seen anyone explain so specifically and clearly that I just always get it. And love how he makes sure everybody gets every part.
I’ve been placed in Intermediate Algebra due to some weird stuff at my community college. I barely scored into Basic Algebra. I’m 30. First time at college, and I’m so nervous. Thanks doc.
Just looking to relearn algebra then work up to trig and calculus, this here seems like it will work great with the Just In Time books that a professor friend recommended me.Thanks for these videos
You are the best Mr. Leonard. I have practiced a lot Factoring by grouping and most of the time end up with similar problem at 1:31 in this video. Mind you i knew what to do...but I really did not know what i was doing. You made it crystal clear. learning a lot from your videos . thanks for the upload. most of the youtube math teaches us what to do with problem...but watching your video teaches me why am i doing it. (sneezed) bless you hahaha
This is an aside but I really like that a math professor can get nearly 300k subscribers (at the time of this comment) and that this is the kind of thing the internet can really do for all of us.
I love your lessons and I know I'm not the first to say that. Also I love this class, these exact same people (I mean voices), they became so close to me, so familiar...💛✨
The best way that I can describe the experience of watching Professor Leonard's lectures is that it feels like binge-watching a great television series.
Professor L, Thank you so much for all you hard work and videos! I am almost through your Pre-algebra Course and was wondering if this Intermediate Algebra is what i should do next??
Be my teacher. You are great at teaching though you are teaching online. I don't space out with you but only with all of my other teachers, you teach people in a very interesting way.
I've never seen that at 9:23 before. That's freaking sweet. And 25:00 is a super important example. And by the way, 1:03:47, what the hell is a sum of cubes?
Sir,kindly slow while putting hands on any single number. I'm from Pakistan . love you sir. Would that you were here! Fate is ever smiling on my face ...My pleasure to attending your great class
I found out about Professor Leonard through his Calculus 1 and 2 lectures. My goal is to like every single video he has ever made.
He deserves it!
@Karanfil
I am currently doing that.
In fact, "Intermediate Algebra" and "Precalculus" are the only playlists that I still haven't watched in full. xD
@@Peter_1986 What about prealgebra?
How's it going?
In fact you start by here
It's really touching to see how much effort Mr Leonard puts in getting his students to 'get it'. A gift, really.
And peeps, 1:10:00, in order to pass calculus, you need to have this factoring stuff down (I know from my own bad experience. Don't sign up for calculus until you have this stuff mastered, seriously). And 1:15:00 is some of the best math studying advice I've ever heard from any instructor, teacher, professor, whatever in my education career; he's dead right. 1:30:00 is factoring by grouping; this is the main method of factoring employed in calculus classes when trying to solve for limits, just a heads up.
Thank you so much this is really helpfull.
Hey buddy. I am struggling with studying. Could you possibly write down a list of pre-calculus topics that are crucial for calculus?
@@user-qy6tu9ip9v Professor Leonard has a whole playlist on his channel for that. Should be covering everything.
@@benjamin-rh7rn Yeah I'm halfway through the playlist. Thanks buddy.
@@user-qy6tu9ip9v how long did it take you to get through the playlist?
This professor is an excellent teacher. I find myself not attending my own class. Instead I listen to his lectures, follow his examples, and low and behold, I GET IT! Thank God for Professors like Professor Leonar. I wish he was a professor at my school!
God is irrelevant.
@@Bilbus7 No, you are irrelevant.
@@Bilbus7 we get it, you're atheist
Professor Leonard says "Raise your hand if you understand..." I'm over here raising my hand : )
Lol! I'm here answering questions out loud and raising my hand as well. This guy is seriously a life saver during this quarantine!
LMAO...same!!
OMg me too hahaha
he's graceful, humble and sharp as hell. this is instantly obvious.
Who's learning from this legend while in quarantine
Yes bob joe he is a legend
anybody knows why it starts at 6.1 and not chapter 1?
@Albi Marku I see, I thought intermediate algebra started in chapter 1. Have you found any good textbook or online worksheets to practices the content he teaches?
@@roblox21242 the Textbook is "Beginning and intermediate algebra by McGinnis, Terry Hornsby, John Lial, Margaret L 6th or 5th edition """
@@whitebeardpirates7551 Thanks hero ❤
Ive passed this link to all my classmates, you have taught us more with such nonjudgmental patience, than our own instructor. Thank you from New York.
everyone says such nice things and i will not be different! Sir your patience when teaching is commendable! i am not a math guy and am going back to school for business after 15 years, your videos are actually making me enjoy math. i can't thank you enough!.
Thanks to this sir, Math is my new hobby
His enthusiasm for math is contagious! I actually enjoy learning about factoring.
Amazing teacher........I've learned so much watching your videos!!!!! Thank You!!!!!
hi
You start learning and liking and subscribing from here
czcams.com/video/1Kie270BgOo/video.html
Hats off to you sir, I swear to God if you were my professor I would love Math and be waiting for the next class. Unfortunately, it's the opposite and the one I have is old and doesn't explain a lot, especially for those who graduated high school in different countries and go study abroad like me. I'M SO HAAAAAAPY THAT I FOUND YOUR CHANNEL.
I just want to thank you for your videos! Your videos are well explained and I know your students are fortunate to have you as a teacher. After watching your videos, I was able to ace the Accuplacer. After taking that test, I felt so proud of myself because my time spent watching your videos was rewarded. Keep doing what you do and trust me, you helping a lot of people out there including me.
I'm taking Math 56 at a CUNY college, and I swear to you I've learned more watching your videos than actually being in my professor's class.
Professor Leonard is truly an amazing teacher, his teaching methods is what I wish all my professors could do. He explains everything really thoroughly to make you better understand! And you can tell he loves his job and cares for his student, on top of that, he's definitely a looker! His wife is really lucky! But thank you for all that you do and putting the time to upload your videos, I feel like I'm a part of this class from where it's definitely helping me with my online class.
Professor Leonard,THANK YOU SSSOOOOOOOOO MUCH!!!!!! You are a true life saver! I am currently enrolled in MAT/117 at UOP and you are thee main reason why am going to pass this class. Thank gods that I found your youtube page from a google search. You make learning math exciting. Thank you for turning on the lights for me. Because before I was in the dark. Thank you for the clarity.
Did you pass it?
@@kaplishk Dude's probably finished his degree a while back already
Fantastic thanks! I'm 34 and pursuing my degree while on active duty. I've been super intimidated by math. These lectures gave me confidence.
48:00 is also really a very important and subtle point. Since we distribute to get 6x+14, we don't include a variable in our GCF because 3x+7 is supposed to be thought of as a number, not a variable. It's written as 3x+7 because we are assuming this number is any number in existence plus seven. However, it's still one number, and multiplying it by 2 doesn't change that. So the question becomes, how do you multiply when you don't know the number before you multiply? The answer is distribution. This is the whole point of distributing. The whole point of factoring is to figure out what two numbers were multiplied together if all you can see is the finished product of multiplying.
So, 2(3x+7) = 6x+14. In this case the result of multiplication is 6x+14. If we ask ourselves what was multiplied together to give 6x+14, the answer is 2(3x+7). Notice that 2 is the GCF of 6x+14. The whole point of finding the GCF is to be able to figure out what two numbers were multiplied together. As you might have guessed, 2(3x+7) is 6x+14 factored. And that's the whole point of factoring, and exactly how and why it works the way it does.
So, I started watching another one of his videos while doing my homework (haven't been in math in nearly 10 yrs, now taking stats.) Kept the video playing because I enjoyed the way he explained things. Even if I already knew it!
So i was supposed to take intermediate algebra at my college, and the class is too expensive, i thought it woukd be best to get a free book, and learn myself from different professors on youtube. Im so happy that i found this professor! He explains things so well, and to where i would understand! I already know some of these things, but it is a huge refresher!
I was really dumb at maths.. Didn't know how to even divide something properly but thanks to Mr Leonard.. I'm quite comfortable now in maths.. God bless you professor
I don't understand rationalizing the denominator, dealing with conjugates, simplifying complex fractions.
@Professor Leonard I know this is old content and I hope you get a chance to read this.. but this has helped me greatly! I am 25 years old and I haven't been in school for so long and math was my worst subject!! You broke this down so beautifully I am going to college to become a game developer in a few months and I commend you for creating this amazing youtube channel and I am starting to find some love for math and the magic it brings to this world math is so miss understood and how important it is to us. I thank you Leonard I am very appreciative of you and your amazing work.
its been 5 years are you a game developer?
Now, I don't have to pay for a tutor.
Rey De Guzman yeah true my goal is to donate to this man once i get a job
This is my first video of yours and WOW, I'm in between semesters and nearly failed math, tis is GOLD.
Even though I graduated long time ago, I watched your lectures which helped me refresh my knowledge and gain a lot of benefits.
So thank you Leo.
I'm so happy to begin this series. Thank you so much for all your passion and hard work ❤
He is SO thorough in his explanations and very easy to follow.
I love your style of teaching! You teach where I’m actually LEARNING & questioning why this is that or this to make it make sense! I’m thankful to have found your channel.
re-constructing my math skills again from going back to basics. I admit,my strong point is science but I'm not ashamed to be a beginner on mathematics. Hopefully after a year,I'll be good on my diff calc.
Thank you for making these from Winnipeg RRC
Going over Pr Leonard's playlists again, this time focusing on arithmetic, number theory and patterns to solidify my foundation of Discrete Math.
Passed the Calculus track (Pre-Calc, Calc I, Calc II), and Linear Algebra, but Discrete Math kicked my butt. Simply couldn't do proofs, because I had lost my affinity with basic numbers and the WHY of doing certain calculations _this_ or _that_ way. Hopefully going this far back in times (even relearning simple addition and multiplication) is going to help me
This is so clear. I'm actually doing this lectures in order to proceed with Linear Algebra, Abstract Algebra, Trigonometry and Calculus
I know this is probably an old video, but he reminds me of my Beginning Algebra instructor that I had Spring Semester 2022.
He's on point like my instructor and made it easy for me to understand!
I wish you could be my professor.
What an amazing teacher, I am truly impressed! I will be sharing this with my friends in class
You're the best CZcams tutor ever....
You deserve to be called a Prof. 100%
unlike some we pay money to and still don"t get what we should
Mr. Leonard has a very interactive way of explaining the concepts and makes so fun to listen, man I also wish he was a teacher at my school. Thank you for what you do.
this was really helpful to me cause im doing this now and you explain way much better than the instructor i have now so thank you
I literally love his way of teaching never seen anyone explain so specifically and clearly that I just always get it. And love how he makes sure everybody gets every part.
You deserve over millions of followers you explain so thoroughly
So glad I found this. Many teachers have tried to teach me this but it never made sense. Thanks so much!
He really is the best math professor I've seen
i just started Pre-Calc and realized I was rusty on my factoring. Thanks for the video!
I would love to see you teach Trig. Love the videos.
Brillant professor!
Professor Leonard You are an amazing teacher!
This man has possibly saved my Grade in pre Cal!!!!
Professor Leonard is the Bob Ross of Lecturing.
I needed that earlier this year. Had to drop algebra. Now it looks like am ready to take it on again. Thanks to this professor. Glad I found this🙏🏿
Great teacher explains everything thoroughly.
He is a good to look at and his videos are worth to look at ...great combo!
Can I just give this guy my tuition money? I learn more from him that college lol
I’ve been placed in Intermediate Algebra due to some weird stuff at my community college. I barely scored into Basic Algebra. I’m 30. First time at college, and I’m so nervous.
Thanks doc.
Very good lecture need to spread the word so more people can subscribe
you are amazing i have been out of school for 9 yrs this is saving me in math 1414 pre cal
Just looking to relearn algebra then work up to trig and calculus, this here seems like it will work great with the Just In Time books that a professor friend recommended me.Thanks for these videos
Im legit watching this and learning for fun!
the Textbook is "Beginning and intermediate algebra by McGinnis, Terry Hornsby, John Lial, Margaret L 6th or 5th edition """
Professor Leonard is the BEST! My kids love him!
I want t say a big thanks for all your help. I just took my test and I am excellent. God bless you!!!!!!
Great video and explanation, we have been watching your videos and learned a lot!
Unequivocally, this dude is an awesome teacher.
Taking algebra this semester... i'm gonna watch your entire intermediate Algebra series before my term starts.
You are the best Mr. Leonard. I have practiced a lot Factoring by grouping and most of the time end up with similar problem at 1:31 in this video. Mind you i knew what to do...but I really did not know what i was doing. You made it crystal clear. learning a lot from your videos . thanks for the upload. most of the youtube math teaches us what to do with problem...but watching your video teaches me why am i doing it. (sneezed) bless you hahaha
He explains it so easy that it makes me feels like a pro and as if I already know it!
God bless you!! Thanks for posting your videos. You are really helpful.
Thank god for this guy!!! Amazing teacher. Thank you!
This is an aside but I really like that a math professor can get nearly 300k subscribers (at the time of this comment) and that this is the kind of thing the internet can really do for all of us.
I just subscribed and you are an amazing teacher I wish you were my professor 👍
I am taking Advanced Calculus and watching this :)
Did you get boned? Or did you do well?
I love your lessons and I know I'm not the first to say that. Also I love this class, these exact same people (I mean voices), they became so close to me, so familiar...💛✨
The best way that I can describe the experience of watching Professor Leonard's lectures is that it feels like binge-watching a great television series.
Professor L, Thank you so much for all you hard work and videos! I am almost through your Pre-algebra Course and was wondering if this Intermediate Algebra is what i should do next??
Thank You so much Sir
THis is a great video. The professor explains really good ......good job !
Thanks alot! Learnt alot of new things I've never known. Makes things clearer now.
Can you please recommend a textbook that corresponds with this series of lectures please? Primarily so I can do practice problems
Be my teacher. You are great at teaching though you are teaching online. I don't space out with you but only with all of my other teachers, you teach people in a very interesting way.
Let's go on with this series as well :D thank u Leo for all the effort
Im taking math 98 @ college. Is this playlist the correct videos I should watch?
BEST PROFESSOR EVER!
This helps me so much I'm taking math 055 at Red rocks CC in colorado
kick ass vid!!! The best I have seen!
Thanks man, seriously you are a great teacher.
Awesome teacher. I fell like I'm in the class. Would be a perfect online teacher or example modules for online class
The best math professor ever = Leonard!
It's worth spending hours finding a great teacher in youtube
got me to do the exercises as well and while trough youtube, great professor :)
Homie broke it down like whaaaat!!! Loving it!
This guy is a gifted teacher 👏
Thanks wonderful teacher, what a blessing!
Hot math teacher !!! Makes math tolerable, yes I can learn this way. More math please.
i feel like i know what i am doing. this guy is great
I've never seen that at 9:23 before. That's freaking sweet. And 25:00 is a super important example. And by the way, 1:03:47, what the hell is a sum of cubes?
The answer at 1:12:13 is amazing. That the teacher keep s going until the student gets it.
Sir,kindly slow while putting hands on any single number.
I'm from Pakistan .
love you sir.
Would that you were here!
Fate is ever smiling on my face ...My pleasure to attending your great class
Helpful. Thanks Professor Leonard.
Excellent lesson. My 61 year old brain picked it up quickly and now I wish I had learned it back in school. Oh well.
Thank you so much from California~!
I am just starting this course, will see you the other side.