40:23 Thanks for doing the hard problems. I have this exact issue; Instructor will go over the easy problems in the lecture and provide us videos to review and then we get to the homework that the instructor created themselves and ill run into problems that aren't even explained in the lecture or videos. Thank you
I just wanted you to know that when you said, "you're gonna write your factors", I didn't say, "you can't make me". I said, "I already did that." And I was super proud of myself when you called it out.
your videos are not to long. they are perfect. you are the reason I have an A in my class. Thank you. if it wasn't for you I know I would be struggling.
28:45 It indeed gave me the math chills! It's awesome how all these things are coming together, even stuff from Intermediate Algebra interplaying at this point, that's crazy! Thank you Prof!!
Never thought I would one day start thinking doing math is fun. Maybe because these videos help me understand everything and I don’t really hate it the way I used to. Thank you so much professor Leonard!!! I will always be grateful for this.
Your videos are amazing. You have single-handedly taught me math and in a way which makes me not just think "oh this is easy now" but "oh this is awesome! I love math!"
Hey Prof, I wanted to thank you. I’m an old military guy being sent through college for vocational rehab (disabled vet being retrained by the VA). My precalculus professor is a little less than articulate. Mostly saying things like, “I really disagree with how the book does this, I’m going to show you how I expect you to do it.” Then proceeds to do it over the projector, skipping parts he does in his head explaining that we know that part and leaves an entire classroom scratching our heads. My biggest problem is that half the time I don’t even understand what the point of an exercise is or what the desired output we are aiming for. Your channel has been immensely helpful in explaining what I’m reading in the book which is all that matters at this time to me. This is all about building a base for the next level, not pleasing the current professor. As far as minding your Ps and Qs, I can clarify that one. It is a nautical term. In the days of sail when sailors pulled into port the bars would sell the booze in pints (Ps) and quarts (Qs). The barkeep would maintain a list of the sailors through the week, or what period of time they worked before receiving pay (each establishment had their own rules) and when a sailor received his pay he was expected to go to the bar and settle up for the tab based on the number of Ps and Qs recorded on his account. Some less than honest bar owners would add some Ps and Qs to a sailor’s tab. A seasoned sailor would advise a young sailor to mind his Ps and Qs to make sure the barkeep wasn’t trying to slip extra charges on his bill, or stick someone else’s drinks who didn’t pay in order to not lose money (as still happens today).
That's interesting. I read somewhere else that P's and Q's stood for the sailors' peacoats and queues. Something to do with looking sharp. Anyways, hope you're doing well now and that your Precalculus professor is not giving you too much trouble!
@@rosepierce9382, thank you for the pleasant thoughts first thing when I wake up this morning. I’ve never heard the “pea oats and queues” version before. I will definitely read on that. When I was in the Navy, we were taught in our maritime history classes about the “pints and quarts” version, but that’s not insisting the U.S. military has not been incorrect before. Also since the saying was passed down, I believe, from the British Navy, it’s certainly worth looking into what their take on it is. No worries on the pre-calculus. I managed to wrap that up and made it through calculus 1 unscathed. It’s smoother sailing at this point. I do hope you have a wonderful day. I’m off to school now.
@@josh8494 Didn't think you'd reply! I might be wrong about the P's and Q's. That's great you got through Calc 1! I am preparing for it right now. Your story is inspiring. It's nice when random strangers like you make my day. I wish you nothing but the very best in life. Stay blessed and much love!
God Bless you dude. I am watching this at midnight, and my professor did not go through the descartes' rule of sign for this. Thank you, this really helped me understand how to do the problems
Never gave my thanks, you helped me ace calc2 and my professor was blatantly senile. Thank you for all you do, we really all appreciate you and see you as our math dad. We appreciate you!
thanks for taking the time to explain and for showing hard exercises. it is true that most professors just work with the simples and easier exercises in class cuz they want to end the class on time and to cover as much chapters as possible instead of taking more time in explaining it [i know they have an agenda to follow, but man it sucks that the school calendar don't actually allow for more room to explain some topics in class. i know professors offer office hours, but sometimes those office hours conflicted with other classes].
This is an incredible video. Holy cow. Some of the most exciting math yet! Its like the rest have been practice and now it's game time and he's the coach that I want
I had just read a chapter on this and my head was swimming on how to put all the concepts together. This was a great demonstration of how to use the whole bag of tricks to tackle a problem.
Thank you so much for these videos, Professor Leonard! After thoroughly studying with your videos over the weekend, I was able to ace my next Precalculus test with minimal confusion on the concepts being taught. I really agree with what you said regarding not being taught everything in the best manner in class at times and appreciate you making this channel and these videos for students like me to learn from and connect the dots. You're a lifesaver!
Professor Leonard, thank you for an incredible explanation of Rational Zero Theorem and its impact on factoring complex polynomials. Synthetic Division is also important when using this important theorem in mathematics. I really enjoy this lecture/video and its powerful analytical makeup.
Funny thing is I did the second way first. I paus the videos and attempt the problems first to see if I can get it and I ended up finding the fraction second. When I watched and saw you did the -1 second I face palmed at doing an obvious easer one than what I did. Good to know I did it correctly though.
God evening sir , I am really attached to you for maths I have recently passed 10th grade and I am working on forming the equation which could explain the rate of change of energy in the universe and being in a lower grade I was not knowing the deepness if graphs , but , I watched your lectures and finally formed the equation , moving my research ahead ...... " THANK YOU SO MUCH SIR "☺️☺️
Re: 40:39 These videos should be the gold standard of what should be taught in a classroom. Anything less is potentially cheating students out of what they need to know.
I am waiting for trigonometry I am very galad to study trigonometry with prof. Leonard I wish you prof. Leonard always happy and keep health It's most important
Yeah man, I have always dreaded how trig is taught in indian schools, I can't say about other places, thus I am always on my toes for trig lecture notification
Professor, we've gone over rational functions in the past in the Intermediate Algebra course. Is precalculus a continuation of that particular subject, or can one skip it and move on to exponentials and logs? Also, about the latter two, is precalculus expanding on the knowledge, or is it more of a revision? Much love from Sweden. You're the best teacher I've ever had.
I heard you say that grouping only works up to 4 terms, but in the last problem I used grouping to solve the polynomial. I rewrote it as x^4(2x-1) + 24x^2(2x-1) - 25(2x-1) -> (2x-1)(x^4 + 24x^2 - 25) and got precisely the right x-intercepts. I even undid my factoring to see if I would get the original polynomial and sure enough I did. Could you explain why you've said that you can group only up to 4 terms, or if I misunderstood your words (most likely the case), thanks.
they say that these are ''too long''!? they be like ''show me how to go from basic math to calculus 3 in five minutes or I'm done with this video''. to truly know is to put the time in! foot note: you can go to settings and set the speed to 2x if you want him to sound like a chipmunk.
what happens if you factor and get a quadratic, you are unable to factor it using the diamond method, so you use the quadratic formula and you get a root. is that an x-intercept?
So the problem that you worked out twice that starts at 1h 2mins. I paused it to see if I could do it on my own. I grouped the terms to pull the (2x-1) out. Professor, is there any reason why you couldn't or shouldn't do that? I got the same answer.....but sometimes that coincidentally happens. Anybody know?
![Noob To Max With DRAGON REWORK In Blox Fruits [FULL MOVIE]](http://i.ytimg.com/vi/LnBMOinoOvA/mqdefault.jpg)
40:39 Who on earth would complain that your videos are too long? That's like saying that you've got too much money in the bank.
If someone is complaining that Prof Leonard's videos are too long, they don't want to win.
40:23 Thanks for doing the hard problems. I have this exact issue; Instructor will go over the easy problems in the lecture and provide us videos to review and then we get to the homework that the instructor created themselves and ill run into problems that aren't even explained in the lecture or videos. Thank you
I just wanted you to know that when you said, "you're gonna write your factors", I didn't say, "you can't make me". I said, "I already did that." And I was super proud of myself when you called it out.
😂good for you
Lol, he was right. When everyhing came together at 28:45 I felt the math chills at how everything just connected
I know what you mean!
your videos are not to long. they are perfect. you are the reason I have an A in my class. Thank you. if it wasn't for you I know I would be struggling.
28:45
It indeed gave me the math chills! It's awesome how all these things are coming together, even stuff from Intermediate Algebra interplaying at this point, that's crazy!
Thank you Prof!!
Wow, the Prof is just pumping content out like a mad man the last few days! Awesome stuff! Thanks again, Professor Leonard. You da man!
31:00 yes! Thanks for all the bubbles of understanding!
Never thought I would one day start thinking doing math is fun. Maybe because these videos help me understand everything and I don’t really hate it the way I used to. Thank you so much professor Leonard!!! I will always be grateful for this.
Videos are not long at all, they are just right for the amount of detail you explain things , thank you prof
Sir, you are one of the most underrated professors that I've ever seen
Your videos are amazing. You have single-handedly taught me math and in a way which makes me not just think "oh this is easy now" but "oh this is awesome! I love math!"
Hey Prof, I wanted to thank you. I’m an old military guy being sent through college for vocational rehab (disabled vet being retrained by the VA). My precalculus professor is a little less than articulate. Mostly saying things like, “I really disagree with how the book does this, I’m going to show you how I expect you to do it.” Then proceeds to do it over the projector, skipping parts he does in his head explaining that we know that part and leaves an entire classroom scratching our heads. My biggest problem is that half the time I don’t even understand what the point of an exercise is or what the desired output we are aiming for. Your channel has been immensely helpful in explaining what I’m reading in the book which is all that matters at this time to me. This is all about building a base for the next level, not pleasing the current professor.
As far as minding your Ps and Qs, I can clarify that one. It is a nautical term. In the days of sail when sailors pulled into port the bars would sell the booze in pints (Ps) and quarts (Qs). The barkeep would maintain a list of the sailors through the week, or what period of time they worked before receiving pay (each establishment had their own rules) and when a sailor received his pay he was expected to go to the bar and settle up for the tab based on the number of Ps and Qs recorded on his account. Some less than honest bar owners would add some Ps and Qs to a sailor’s tab. A seasoned sailor would advise a young sailor to mind his Ps and Qs to make sure the barkeep wasn’t trying to slip extra charges on his bill, or stick someone else’s drinks who didn’t pay in order to not lose money (as still happens today).
That's interesting. I read somewhere else that P's and Q's stood for the sailors' peacoats and queues. Something to do with looking sharp. Anyways, hope you're doing well now and that your Precalculus professor is not giving you too much trouble!
@@rosepierce9382, thank you for the pleasant thoughts first thing when I wake up this morning. I’ve never heard the “pea oats and queues” version before. I will definitely read on that. When I was in the Navy, we were taught in our maritime history classes about the “pints and quarts” version, but that’s not insisting the U.S. military has not been incorrect before. Also since the saying was passed down, I believe, from the British Navy, it’s certainly worth looking into what their take on it is.
No worries on the pre-calculus. I managed to wrap that up and made it through calculus 1 unscathed. It’s smoother sailing at this point.
I do hope you have a wonderful day. I’m off to school now.
@@josh8494 Didn't think you'd reply! I might be wrong about the P's and Q's. That's great you got through Calc 1! I am preparing for it right now. Your story is inspiring. It's nice when random strangers like you make my day. I wish you nothing but the very best in life. Stay blessed and much love!
God Bless you dude. I am watching this at midnight, and my professor did not go through the descartes' rule of sign for this. Thank you, this really helped me understand how to do the problems
Never gave my thanks, you helped me ace calc2 and my professor was blatantly senile. Thank you for all you do, we really all appreciate you and see you as our math dad.
We appreciate you!
thanks for taking the time to explain and for showing hard exercises. it is true that most professors just work with the simples and easier exercises in class cuz they want to end the class on time and to cover as much chapters as possible instead of taking more time in explaining it [i know they have an agenda to follow, but man it sucks that the school calendar don't actually allow for more room to explain some topics in class. i know professors offer office hours, but sometimes those office hours conflicted with other classes].
This is an incredible video. Holy cow. Some of the most exciting math yet! Its like the rest have been practice and now it's game time and he's the coach that I want
I had just read a chapter on this and my head was swimming on how to put all the concepts together. This was a great demonstration of how to use the whole bag of tricks to tackle a problem.
Thank you so much for these videos, Professor Leonard! After thoroughly studying with your videos over the weekend, I was able to ace my next Precalculus test with minimal confusion on the concepts being taught. I really agree with what you said regarding not being taught everything in the best manner in class at times and appreciate you making this channel and these videos for students like me to learn from and connect the dots. You're a lifesaver!
I am glad your videos are long because you explain all the details and are repetitive which helps to drill it into my brain lol.
The legend, Professor Leonard!
40:29 the third problem felt like a dark souls boss at first but Leonard explained it very well as always
Professor Leonard, thank you for an incredible explanation of Rational Zero Theorem and its impact on factoring complex polynomials. Synthetic Division is also important when using this important theorem in mathematics. I really enjoy this lecture/video and its powerful analytical makeup.
This is exciting! Cool to see all the concepts come full circle here.
Oh my God you're videos are really really helpful thanks a million professr
You're a life saver!!!!!!!
Thank you for explaining this in such an approachable way!
Thank you! It feels so good to be able to solve these demons.
Prof Leonard is God sent. Thanks for your videos.
getting some serious math chills
You are the best professor ever!
Funny thing is I did the second way first. I paus the videos and attempt the problems first to see if I can get it and I ended up finding the fraction second. When I watched and saw you did the -1 second I face palmed at doing an obvious easer one than what I did. Good to know I did it correctly though.
Daily uploads for the win prof Leonard!!!
God evening sir , I am really attached to you for maths I have recently passed 10th grade and I am working on forming the equation which could explain the rate of change of energy in the universe and being in a lower grade I was not knowing the deepness if graphs , but , I watched your lectures and finally formed the equation , moving my research ahead ......
" THANK YOU SO MUCH SIR "☺️☺️
What's the equation?
Im so unused to passionate teachers omg! This has really resparked my interest in math, thank you!
Keep doing long videos, it's better than missing points. Btw, great video!
Thank you for the video, Professor Leonard; it was super helpful.🙂
Re: 40:39 These videos should be the gold standard of what should be taught in a classroom. Anything less is potentially cheating students out of what they need to know.
Thank you for all the lessons recently.
“Mind your P’s and Q’s” I heard came from a British pub saying: “Mind your Pints and Quarts.” 12:50
The thumbnail nail pic closely resembles how the professor holds his whiskey and smokes his cigar
I love how you have 3 of the same shirts in different colours.. like literally Same
Amazing work as usual !!
I almost forgot about this theorem. Highly useful!
Thank you so much for all the work you do with these videos. I am really learning a lot and this video in particular was great.
Doing great sir, keep doing
Great one!
Great work
Excellent teacher
You are the best ever ever ever ever ever ever ever ever
AWESOME VIDEO! Thank you!
The Descartes rule is nice. Good to have constraints to simplification. Not seeing Vieta's formula, but perhaps that's too formal?
Sir You are the best I'm a huge fan Love from Pakistan ❤️
I am waiting for trigonometry
I am very galad to study trigonometry with prof. Leonard
I wish you prof. Leonard always happy and keep health
It's most important
trig is coming soon! as soon as this college algebra stuff is all done :)
Professor Leonard yay ! Thank you 🙂
@@ProfessorLeonard thanks for reply
I am always waiting for your reply
Now I am happy
Keep safe and healthy
Yeah man, I have always dreaded how trig is taught in indian schools, I can't say about other places, thus I am always on my toes for trig lecture notification
WOOHOO THE GOAT PROFESSOR
you are always Great alwaaaaaaaaaaays , Keeeeeep going prof ♥♥♥♥♥♥♥ you simple the harder things to easiest things to understand it very well ♥♥♥
Clicked on this so fast. Thank you professor!
That's such a cute hairstyle tanya! 😋
Thank you sir
professor leonard is literally superman
Professor, we've gone over rational functions in the past in the Intermediate Algebra course. Is precalculus a continuation of that particular subject, or can one skip it and move on to exponentials and logs? Also, about the latter two, is precalculus expanding on the knowledge, or is it more of a revision?
Much love from Sweden. You're the best teacher I've ever had.
Hi there! This expands greatly on the idea of rational functions, especially when it comes to their graphs. Hope this helps!
@@ProfessorLeonard Thank you, professor Leonard!
I tried skipping descartes rules of signs and it came back at me! back to that video haha
Legit same lol
Professor, could you please complete the Statistics playlist.
Please professor, complete the Statistics Playlist
I heard you say that grouping only works up to 4 terms, but in the last problem I used grouping to solve the polynomial. I rewrote it as x^4(2x-1) + 24x^2(2x-1) - 25(2x-1) -> (2x-1)(x^4 + 24x^2 - 25) and got precisely the right x-intercepts. I even undid my factoring to see if I would get the original polynomial and sure enough I did. Could you explain why you've said that you can group only up to 4 terms, or if I misunderstood your words (most likely the case), thanks.
"too long" ? ? ? And what could be removed? Keep the complete coveragel!
Haa-Haa, was that G C F natural?
Sir do u ever notice that you're a legend?
When you get to a quadratic then use the quadratic equation, not sure if it will yield any irrationals
Sir (professor) Thank you for all these Awesome Knowledge.
Can You tell me Which Book are you using For Precalculus?
they say that these are ''too long''!? they be like ''show me how to go from basic math to calculus 3 in five minutes or I'm done with this video''. to truly know is to put the time in!
foot note: you can go to settings and set the speed to 2x if you want him to sound like a chipmunk.
I tried doing that and he sounded too funny lol
Damn, this was complicated lol, it's starting to make sense tho.
Please do some more differential equations videos. Thank you, professor!
Yeah, we need it
Decarte's rule of sign it is work for pplt 2nd dergee ?
Professor, please complete your statistics playlist. 🙏
Professor, are you still planning on doing Linear Algebra?
thank you for this!!!!!!!!!!!!
what happens if you factor and get a quadratic, you are unable to factor it using the diamond method, so you use the quadratic formula and you get a root. is that an x-intercept?
Plz..make videos on real analysis..plz
Professor leonard you are help alot
But i request you if you can to start geometery
Why is Superman teaching math?
😂😂😂
So the problem that you worked out twice that starts at 1h 2mins. I paused it to see if I could do it on my own.
I grouped the terms to pull the (2x-1) out. Professor, is there any reason why you couldn't or shouldn't do that? I got the same answer.....but sometimes that coincidentally happens. Anybody know?
Hi Professor Leonard, can you make College Physics series after completed Algebra and Trigonometry (Precalculus) and Linear Algebra?
Please look at The Organic Chemistry Tutor Playlist.
Math guy on steriods, discovering you was great
His physique is definitely achievable naturally
@@user-yh6lr8wy9s I Think he was referring to the rigor of his mathematics.
Is this typically a class people take after Algebra2?
I know it's late, but usually after Trigonometry, or together
😱
Just use a graphing calculator and skip the rest.