i bet out teacher knew it as well but as it were not curriculum it was not on the menu :)
@helpwithmathingКүн бұрын
@rivenoak glad I could offer it then
@bjornfeuerbacher55142 күн бұрын
Another way to do it, without having to guess-and-check: first complete the square, x² - 2x - 48 = (x - 1)² - 49. This is a difference of squares, so it's easy to factor: ( (x - 1) + 7) ( (x - 1) - 7). So the end result is (x + 6) (x - 8). May take a bit longer at first, but if one is used to completing the square, it's quite fast.
@helpwithmathing2 күн бұрын
@bjornfeuerbacher5514 YES! LOVE IT!
@markmurto4 күн бұрын
While you do have some fun facts, the methods are too slow for practical application. Speed and experience is what should be taught after the basic understandings are demonstrated. It is lightening fast to just use the quadratic equation in your head. In the class test, you have to "Show your work." So yes we can play the games with the x and factor method for the teacher. But at work the quadratic is all you need to apply. In electronics, road work, engineering, etc., because the answers are usually complex, thise methods are seldom used.
@helpwithmathing4 күн бұрын
@markmurto you are entirely correct! The Quadratic Formula is best for solving quadratics in the course of your work. Carry on.
@helpwithmathing4 күн бұрын
@markmurto. kzbin.info/www/bejne/qYGZmGx9rL1_nbc
@markmurto4 күн бұрын
@helpwithmathing Had no doubt that you know the quadratic equation. .I believe you are quite brilliant.
@helpwithmathing4 күн бұрын
@markmurto well thank you kindly sir!
@christopherellis26634 күн бұрын
6 minus 8 is minus eight. There is no electromagnetic field involved.
@helpwithmathing4 күн бұрын
@christopherellis2663 I would love to respond to your comment, but I'm not sure I understand it! Please feel free to further explain your comment/critique/addition/quip ;)
@baselinesweb3 күн бұрын
meth minus coke = this comment.
@helpwithmathing3 күн бұрын
@baselinesweb this made me literally laugh out loud: thank you for the morning chuckle!
@Pootycat83592 күн бұрын
@@helpwithmathing He's describing a technique that involves manipulation of the Viscous & Resinous Fluids. Unfortunately, this method only works if it's performed on a Moonless night at a crossroads.
@helpwithmathing2 күн бұрын
@Pootycat8359 you folks are making my days over here. Thank you for the chuckles!
@silvermine203313 күн бұрын
Very helpful. Thank you!
@helpwithmathing13 күн бұрын
@silvermine2033 Nice to hear from you again, and so glad it was helpful!
@vespa286013 күн бұрын
Just going to comment, but.....
@helpwithmathing13 күн бұрын
but....? Nice to hear from you, @vespa2860
@johnlakin589528 күн бұрын
This is one of those really helpful and concise videos that you know you can always go back to if you need a bit of a reminder.
@helpwithmathing28 күн бұрын
Yay!! Stay turned: I'm currently editing a video that puts this stuff into practice in some stumper-type homework questions!
@silvermine203329 күн бұрын
Very helpful. Thank You!
@helpwithmathing29 күн бұрын
I'm so pleased you found it helpful!
@johnlakin5895Ай бұрын
Are you really a professor? Na you can’t be, you’re not old enough.
@helpwithmathingАй бұрын
@johnlakin nope, hilariously I am a professional actress (I'm also a certified high school English teacher, but I never did anything with that degree). I just love math, and making these videos seemed like a good way to use my loves and my skills to give back a bit in this crazy world and help people who can't afford a high priced tutor.
@johnlakin5895Ай бұрын
@ What a lovely thing to think, and now l will looking out for you every time l watch the telly.
@naderhumoodАй бұрын
Lovely professor.....you outdid yourself today. Thank you very much indeed.
@helpwithmathingАй бұрын
@naderhumood this comment just made my day. Thanks so much for watch and giving feedback!!
@johnlakin5895Ай бұрын
Would the contents of this video be considered as advanced maths?
@helpwithmathingАй бұрын
@johnlakin5895 In US courses, students encounter "i" in their second Algebra course, so usually when they are 14-15 years old.
@johnlakin5895Ай бұрын
@ 14-15 yr olds, blimey, that puts me about 46 yrs out of date.😢
@georgeh1352Ай бұрын
I like this method of factoring. I am an old man revisiting Math, thanks for the videos.
* XX - 6X - 16 16 = 2 x 8 = 4 x 4 8 - 2 = 6 = ( b) * 8 X 8 - 6 x 8 - 16 64 - 48 - 16 = 0. * 2 x 2 -6 x 2 - 16 # 0 (-2)(-2) - 6(-2) - 16 4 + 12 - 16 = 0 X' = 8 , X" = - 2 .
@helpwithmathingАй бұрын
Thank you so much for these demonstrations!
@ngocdo5687Ай бұрын
XX - 10X + 24 * 24 = 2 x 12 = 3 x 8 = 4 x 6 . 12 - 2 = 10 = (b) ** 12 x 12 - 10 x 12 + 24 144 - 120 + 24 # 0 ** 2 x 2 - 10 x 2 + 24 4 - 20 + 24 # 0 (-2) x (-2) - 10 x (-2) + 24 4 + 20 + 24 # 0 ** 6 + 4 = 10 = (b) 6 x 6 - 10 x 6 + 24 36 - 60 + 26 = 0 4 x 4 - 10 x 4 + 24 16 - 40 + 24 = 0 *** X' = 6 , X" = 4 ./.
@ngocdo5687Ай бұрын
* XX - 3 X - 18 18 = 2 x 9 = 3 x 6 6 - 3 = 3 = ( b) 6 x 6 - 3 x 6 - 18 * 36 - 18 - 18 = 0 (-3)x(-3) - 3 x(-3) - 18 * 9 + 9 - 18 = 0 X' = 6 , X" = -3./.
@helpwithmathingАй бұрын
Thank you so much for these demonstrations!
@helpwithmathingАй бұрын
Thank you so much for these demonstrations!
@helpwithmathingАй бұрын
Thank you so much for these demonstrations!
@naderhumoodАй бұрын
Vedio is great, however your audio is not clear .Thank you very much indeed.
@helpwithmathingАй бұрын
Yikes, OK. Thanks for letting me know and I'll look into what might be causing problems. I'm not experiencing any audio glitches when I play it, but I will reach out to KZbin and see what I can figure out! Thanks for watching!
@naderhumoodАй бұрын
Lovely channel. Thanks for posting. I love your approach.
@helpwithmathingАй бұрын
I'm so happy you are enjoying the videos!!
@johnlakin5895Ай бұрын
So once you’ve learned synthetic division, do you never have to use long division again?
@helpwithmathingАй бұрын
@johnlakin5895 Coooooorect. Unless you are in a first level Algebra class, in which case you will be forced to learn long division first. To streeeeech your brain.
@christopherhemley9217Ай бұрын
Help
@helpwithmathingАй бұрын
@christopherhemley9217 !! That's what I'm here for!! Which part was troublesome? The initial step of how to figure out what you multiply the first term by, or the process of multiplying through, or why these are the steps to take? Would it be helpful if I did an example of long division with numbers first, then showed how you take the same steps but with algebraic expressions? Help me help you :)
@helpwithmathingАй бұрын
@christopherhemley9217 take a look at this video which starts with an easier Polynomial Long Division problem to see if that helps, then try this more advanced one again, then let me know if you need further explanation. I'm here for you!! kzbin.info/www/bejne/n2fTaJmsf8ibbtU
@johnlakin5895Ай бұрын
Love this video, one of my favourites.
@helpwithmathingАй бұрын
@johnlakin5895 I so appreciate your viewership!
@vespa2860Ай бұрын
😃
@helpwithmathingАй бұрын
@vespa2860 I almost published a little card at the beginning of the video that said "This one's for Vespa!!" Thanks for the inspiration!
@johnlakin5895Ай бұрын
Well…l’ve never heard of that one before…l’ll have to decide if it beats the x method now.
@helpwithmathingАй бұрын
@johnlakin5895 What I love about the X Method is it really lays it out HOW factoring relates to multiplying binomials and the four terms that condense to three terms etc. What I love about this new method is how dang simply and quick it is. But it does seem a bit removed from the concepts involved in factoring and FOIL'ing.
@barneyDcaller2 ай бұрын
There is another method on factoring with leading coefficient. Multiply the leading coefficient of x² to the constant. Do the usual factoring, then divide each constants with the leading coefficient of x². If one constant equals the whole number, retain the quotient as a factor. If the other constant is not divisible with the leading coefficient, copy that leading coefficient to x. Ex: 2x²+11x-6 Multiply 2 to -6, x²+11x-12 Factor out: (x-1)(x+12) Divide all constant by leading coefficient 2 from the original equation: (x-1/2)(x+12/2) Simplify: (x-1/2)(x+6)... Carry over the /2 from x-1/2 and transfer the 2 to x Answer: (2x-1)(x+6)
@helpwithmathing2 ай бұрын
@barneyDcaller. This method is really intriguing, and seems to work as long as the leading coefficient is a prime number; I'm wonder how it works when the leading coefficient has multiple factors, such as 6x^2 - 7x - 5. You multiply the 6 times the -5 to get -30, factor to get (x-10)(x+3). Divide each constant by 6 and neither is an integer, nor is the answer (6x-10)(6x+3). How do you adjust this method to still work when the leading co-efficient itself has multiple factors?
@johnlakin58952 ай бұрын
What are asymptotes? And what do they do?
@helpwithmathing2 ай бұрын
OK, @johnlakin5895. video soon, but briefly, asymptotes are lines that a function approaches but never hits. In graphic rational equations, we find the vertical and horizontal asymptotes of a function to help us graph it (look at my videos in the Pre-Calculus play list on graphing rational function). Similarly, if you think of the graph of the trig function Tangent, which is Sine/Cosine everywhere the Cosine function is zero will be an asymptote in the Tangent function since you cannot have a zero on the bottom of a function. That's the quick answer. More soon...
Thank you for posting my requested video…there’s more to it than l thought. Oh well l’ll just have to get my thinking cap on and get stuck in 😊 once again thanks.
@helpwithmathing2 ай бұрын
@johnlakin Keep your questions coming! Very helpful to me!!
@johnlakin58952 ай бұрын
I love algebra, but l’m also curious about calculus..have you any videos about basic calculus?
@helpwithmathing2 ай бұрын
@johnlakin ahhh, I'm going to disappoint you here: I've been keeping pace with my twin 14 year olds' math classes and haven't gotten to reviewing my Calculus yet....that'll be a year + from now. But meanwhile loads of Algebra, Geometry, Trig and Pre-Calculus....
@johnlakin58952 ай бұрын
@@helpwithmathing not disappointing at all, l look forward to all your future posts. Keep ‘em coming thick and fast…😊
@helpwithmathing2 ай бұрын
Will do!
@johnlakin58952 ай бұрын
I’ve just seen this very informative video on parabolas, thank you. Have you ever done a video on when the parabolas,rather than go up or down,come in from the sides? I’ve been looking for a video on sideways parabolas for ages and l just can’t find one.
@helpwithmathing2 ай бұрын
@johnlakin5895. Oh excellent. I have not made that video yet, but it is now next on my list. I should be able to get it published by the end of Monday. Thank you so much for the suggestion!
@helpwithmathing2 ай бұрын
@johnlakin5895. OK, here you go, a video on parabolas that open sideways. Let me know if this is what you were looking for: kzbin.info/www/bejne/emmclah8h5tolac
@johnlakin58952 ай бұрын
When you talk about pre-algebra, algebra 1, 2 etc..where would they be in terms of A levels, O levels and the like.
@helpwithmathing2 ай бұрын
@johnlakin5895. Great questions and honestly, I'm not sure. In the US, math gets divided up by subject matter. An ordinary course of study would be Geometry in the first year of high school, Algebra II/Trig the second year, Pre-Calculus (a very rigorous course looking back at Algebra I and II, Geometry and Trig but taking each subject to its most complicated problems) and then Calculus I and II. Students on an advanced track will start with Algebra II Trig as their first high school year and end at Multivariable Calculus their final year. Students who need more time to achieve will start with Algebra I and end with Pre-Calculus. And Statistics is set aside as its very own course, which can be taken any time after Algebra II. How does that map onto O levels and A levels?
@vespa28602 ай бұрын
@@helpwithmathing O levels were typically taken at the end of secondary school (16 years) A levels were typically where the student concentrated on a few subjects, (usually three) and would be examined at the end (18 years old). I took three A levels (chemistry, geology and zoology) at this age. This was in the mid 70's ! A lot of students still went to the same school (called the sixth form for this age group). I went to a further education college for mine - my school was very small and could not begin to cater for post 16 education. It was expected that all students passed O levels in both English and maths (at least) included in a total of around five O levels to undertake A levels (maths especially, if you were going to study any science subjects. As I understood this video, I'm guessing at O level!
@helpwithmathing2 ай бұрын
@vespa2860 Ah, this is helpful. Thank you!
@silvermine20332 ай бұрын
Very helpful topic to cover. Thank you!
@helpwithmathing2 ай бұрын
@silvermine2033 Nice to hear from you, and so happy it was helpful!
@johnlakin58953 ай бұрын
Why does 2 times the square root of 30 suddenly become 2 times the square root of 3?
@helpwithmathing3 ай бұрын
@johnlakin5895 Yup, you noticed my copying error. Question: I put a subtitle into the video to note that I goofed. It should say, "YIKES! Copying mistake. That should be 30 under the square root sign. So sorry everyone!!" Did that not appear on the screen? Shoot, I'll have to look into why that isn't showing any more. At any rate, yes, good noticing and sorry for the mistake!
@johnlakin58953 ай бұрын
‘Goofed’ l love that, It’s so American…here in the UK l have never heard anyone ever say that they’ve ’goofed’…😊
@helpwithmathing3 ай бұрын
@@johnlakin5895 is that because they use a different word, or because they don't admit mistakes? LOL, just kidding, but truly, I'm really glad you are watching and paying good attention.
@SuperPkd3 ай бұрын
Omg
@helpwithmathing3 ай бұрын
Glad this was happy making!
@SuperPkd3 ай бұрын
@@helpwithmathing very much ur highness
@vespa28603 ай бұрын
Have to watch a few times to get some understanding. You brought up h and k as in the standard equation of a circle. But what do h and k actually mean? Are they just letters assigned to distances for both x and y,, or do they actually refer to a particular name?
@helpwithmathing3 ай бұрын
@vespa2860 This is instructive for me, thank you!, because I actual had a section explaining that (h,k) in a parabola is the horizontal and vertical shift of the (0,0) vertex of the parent equation, but I decided that people looking for information on focus and directrix were probably already familiar with vertex and would be bored. However, I think there is a need to link to a "pre-video" to this one that talks about translations, transformations and reflections specifically for quadratics. I do have this one, which might be a good start until I make a new one: kzbin.info/www/bejne/hJLOZJJ-eqp5i9U
@helpwithmathing3 ай бұрын
@vespa2860 And in terms of what H and K stand for: I can't find any legit explaination, and in different countries they use different letters: some use (m, n). Some posit that H stands for horizontal and K would be vertiKal, but that doesn't sound legit to me. Let me know if your research leads to anything, but otherwise they are just the letters assigned in American math to the horizontal/vertical shifts of vertex in parabolas and centers in Ellipses, Circles and Hyperbolas. (I've got videos on those if you look into the Pre-calculus playlist, but they are very early in my channel and probably could use a refresh now that I've gotten more seasoned at making channel content.
@vespa28603 ай бұрын
@@helpwithmathing Yes, I've seen a and b used here (England). I also figured that h could refer to horizontal, but k! Thought they might be referencing some Latin/Greek origin. but I gave up a few years ago when I was getting nowhere. I'll look at your video linked above again. So thanks for that.
@helpwithmathing3 ай бұрын
No problem. More soon I promise!
@drisslahlou27263 ай бұрын
Discriminant =0 solution= -b/2a
@helpwithmathing3 ай бұрын
RIGHT!!
@drisslahlou27263 ай бұрын
Thanks prof❤
@helpwithmathing3 ай бұрын
@drisslahlou So glad it was helpful!
@johnlakin58953 ай бұрын
Thank you…that video cleared up a few things l wasn’t sure about
@helpwithmathing3 ай бұрын
@johnlakin5895 So pleased to hear that!
@angelsmileyprettyprincess3 ай бұрын
Why not( -12x ) +2x? i.e-12x+2x
@helpwithmathing3 ай бұрын
@angelsmileyprettyprincesss. Thanks so much for asking!! Not only to we need them to add to -10, but we also need them to multiply to positive 24. (-12) x (2) will be -24. So that pairing won't work, leaving us with (-4) x(-6) which both adds to (--10) and multiplies to positive 24. Does that clear that up? If not, ask more questions.
@vespa28603 ай бұрын
5:03 6/4 =3/2
@helpwithmathing3 ай бұрын
GAH! Good catch. Oft, OK, I'll go in an edit as soon as I am able. Thank you as always, @vespa2860
@helpwithmathing3 ай бұрын
OK, @vespa2860 I think I added in a subtitle correction. Again, thanks for having my back!
@vespa28603 ай бұрын
@@helpwithmathing Yes, it works. A small error (flipping the numerator/denominator) which doesn't really change the point you were making (change of form).
@helpwithmathing3 ай бұрын
@@vespa2860 I am always so happy to hear from you. Thanks for continuing to work your way through the channel!