Is it all about pattern recognition? As in part 2 here, "Factoring by grouping". Someone with a good eye for it might directly see that -3 and -1.5 are the roots to that polynomyal (if it equals 0). Because, it's obvious! Someone with a less good feeling might group it to 2x^2+9(x+1) and not easily get any further. I don't see how this is helpful unless assuming some talented intuition for it.
I really struggle with factoring at times, and when I hit up the videos/notes from my useless, unenthusiastic teacher, it all gets more confusing... This video was just pure salvation! You'll have my subscription from now on!
I think it has much to do with getting acquainted with how the numbers themselves are factorized. The even are obvious to us all. Then there are the threeven, the s-even and el-even. ;-) Learning the division column like school learned us the multiplication table helps. To 1% precision (two decimals), learn what 1 divided by every whole number up to 50 is. So that you immediately see that 1/13=0.077. It's not as hard as it looks. Many are multiples of each other. Others have funny patterns. 1/9= 0.111... 1/11=0.0909... And 1/7=0.1428 where 14=2*7 followed by 28=4*7. And it actually goes on for ever! There are more "mysteries" like that. They are at least useful for memorizing. I think that familiarity with the figures themselves helps finding grouping of factors that simplifies stuff. But I can tell you, that this is only for the school books! In real life you will NEVER encounter a polynomial with integer coefficients. They will all be rounded averages with different standard deviations from their measurement errors. (And by now AI might've put that stuff on the shelf already)
Thanks for this. I am still having issues with the sum of like terms - I must remember: (-8 +(-8))= 0, not -16! I had to rewind this so many times. I know you wanted a short video, but those logic steps that help fixate the factoring rules were missed.
Method # 7 example #2 = 8X^3 +27 = 8x^3 + 3^3 = (x +3) (2(2x)^2 -3x +9) ; (x+3) [2(4x^2) - 3x +9]I am confused as to which terms to use the cube or the (X+3); I used the logic of having to match the original expression to factor; however, I could not know for sure if this is the final answer, or if I have to use substitution since the new expression has a#1 and has no obvious common factor or long division. I tried both and failed to find original expression. What am I missing?
Oh god i really hope i never have to do this factoring type of long division. It just... It just seems so made up or almost like were compensating for what the human race dont know 😅... Like how is replacing the x for 1 in that equation = to 0... no way, no how. I got 8
If that's the case, what brings you here? If you're retired, maybe there’s something else you’d find more interesting. It’s a common logical fallacy to think, "I didn’t need to use this directly in my life, so it must be useless." But engineers and scientists used these concepts to design and build the very device you’re using to write your comment.
Well, the folks that built your house did, and the ones that built the roads and bridges you drive by, and the ones that made your car, and the one that made your electronic appliances, and so on and so forth. So, I guess you needed it more than you thought you did.
I didn't include the solution to method #7 example #2....can you figure it out? Reply with your answer!
(2x)^3 - (3)^3
a= 2x, b= 3
So the answer is:
(2x-3)(4x^2 + 6x + 9)
Is it all about pattern recognition? As in part 2 here, "Factoring by grouping". Someone with a good eye for it might directly see that -3 and -1.5 are the roots to that polynomyal (if it equals 0). Because, it's obvious! Someone with a less good feeling might group it to 2x^2+9(x+1) and not easily get any further. I don't see how this is helpful unless assuming some talented intuition for it.
Thank you so much Mr. Jensen for making these easy to understand videos! You are a great teacher!!
I really struggle with factoring at times, and when I hit up the videos/notes from my useless, unenthusiastic teacher, it all gets more confusing... This video was just pure salvation! You'll have my subscription from now on!
I think it has much to do with getting acquainted with how the numbers themselves are factorized. The even are obvious to us all. Then there are the threeven, the s-even and el-even. ;-)
Learning the division column like school learned us the multiplication table helps. To 1% precision (two decimals), learn what 1 divided by every whole number up to 50 is. So that you immediately see that 1/13=0.077. It's not as hard as it looks. Many are multiples of each other. Others have funny patterns. 1/9= 0.111... 1/11=0.0909... And 1/7=0.1428 where 14=2*7 followed by 28=4*7. And it actually goes on for ever! There are more "mysteries" like that. They are at least useful for memorizing.
I think that familiarity with the figures themselves helps finding grouping of factors that simplifies stuff. But I can tell you, that this is only for the school books! In real life you will NEVER encounter a polynomial with integer coefficients. They will all be rounded averages with different standard deviations from their measurement errors. (And by now AI might've put that stuff on the shelf already)
It was indeed, the only factoring video ive ever needed
Thank you for the well-explained and easily understood videos, Mr. Jensen. You are the best.
It is the best video about factoring. It's great for refreshing math knowledge.
Could you make a next top 10 about college Calculus? Your videos are so engaging!
Thank you so so much,your labor is invaluable
Not a math student, but thoroughly enjoyed the way you taught👍
Very nice and informative, loved it 🎉
I wish I would have had a math teacher like you!
This video really helped me thank you so much ❤️
I really need this thank you jensen
You have my respect and my time
Student from Bangladesh ❤
Top 10 things to know about set theory 🙏
So helpful
Synthetic division helps me 😅 thanxs u😊
@17:00 As a maths teacher I'm not so keen on saying 'it works'. Instead I would have explained that it works because 7y+-3y=4y and 7y×-3y=-21y²
I'm watching from UZBEKISTAN
Could you please do video on interest and compound interest
Just in time for my test on Monday 🙏
Thanks for this. I am still having issues with the sum of like terms - I must remember: (-8 +(-8))= 0, not -16! I had to rewind this so many times. I know you wanted a short video, but those logic steps that help fixate the factoring rules were missed.
just good to see rational root theorem
Plz make a vd about top 10 must knows about inverse trigonometry
Student from Indonesia❤
Amazing
SFFT is also amazing!
ty :)
Can I ask about the app. Which you use
Integration and Differentiation plzz 🙏
Genius
41:18 2x^2-3x^2=-x^2
It's 2x^2 - (-3x^2) which is why it equals 5x^2
@@MrJensenMath10 ohhhh, now i get it, you applied that one euclide's long division
What i'd like to see is less ads. They really destroy my train of thought.
5:14 did the Y next to 30X⁴ at example 3 vanished or am i missing something
I think that was his cursor.
Student from India 🖤
I am from Kolkata (W.B) bangali and you?❤
Why is the heart black? 💀
@@bebektoxic2136 matching with my 🖤
@@EcoWave07 Bihar
Ya ya , we are everywhere 😭😭😂😂
Method # 7 example #2 = 8X^3 +27 = 8x^3 + 3^3 = (x +3) (2(2x)^2 -3x +9) ; (x+3) [2(4x^2) - 3x +9]I am confused as to which terms to use the cube or the (X+3); I used the logic of having to match the original expression to factor; however, I could not know for sure if this is the final answer, or if I have to use substitution since the new expression has a#1 and has no obvious common factor or long division. I tried both and failed to find original expression. What am I missing?
Thx jensen math Idk 🤷🏻♀️ factoring
For the first method what if they don’t have same gcf and than can we divide with other numbers will that still work?
Minatwar shnkoo 😊😅❤
❤❤❤
PDF of this video plsss it’s a humble request
Probably be faster to take screenshots and save the images to word or to a PowerPoint
12th grade student from Bangladesh 🇧🇩
can someone explain please, how is it negative -7x - 5x = -2x
-7x-(-5x)=-7x+5x=-2x
The long division part is very hard, you got to go slower with more examples
Students from ethiopia 🤗
Oh god i really hope i never have to do this factoring type of long division. It just... It just seems so made up or almost like were compensating for what the human race dont know 😅... Like how is replacing the x for 1 in that equation = to 0... no way, no how. I got 8
Unless.... Since the variables are the same we add the bases? Only way I see it equaling 0 and if that's the case what about the exponents?
Who is watching from Pakistan
Me 😊
Wow you have internet😮
JEE wale
im 46 years old and retired at 30 and i never needed any of this in my life ?
If that's the case, what brings you here? If you're retired, maybe there’s something else you’d find more interesting. It’s a common logical fallacy to think, "I didn’t need to use this directly in my life, so it must be useless." But engineers and scientists used these concepts to design and build the very device you’re using to write your comment.
You didn't but other people needs , math is literally the key of all types of science
Well, the folks that built your house did, and the ones that built the roads and bridges you drive by, and the ones that made your car, and the one that made your electronic appliances, and so on and so forth. So, I guess you needed it more than you thought you did.
Your career has been very short apparently. What have you been doing? Footballer?
@@JeanMarieGalliotlmao