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)
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.
Not a math student, but thoroughly enjoyed the way you taught👍
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)
Could you make a next top 10 about college Calculus? Your videos are so engaging!
Thank you so much Mr. Jensen for making these easy to understand videos! You are a great teacher!!
It is the best video about factoring. It's great for refreshing math knowledge.
Thank you for the well-explained and easily understood videos, Mr. Jensen. You are the best.
Very nice and informative, loved it 🎉
Thank you so so much,your labor is invaluable
Student from Bangladesh ❤
You have my respect and my time
I really need this thank you jensen
This video really helped me thank you so much ❤️
Synthetic division helps me 😅 thanxs u😊
Top 10 things to know about set theory 🙏
Just in time for my test on Monday 🙏
Student from Indonesia❤
just good to see rational root theorem
Amazing
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 😭😭😂😂
SFFT is also amazing!
Integration and Differentiation plzz 🙏
Students from ethiopia 🤗
12th grade student from Bangladesh 🇧🇩
Can I ask about the app. Which you use
For the first method what if they don’t have same gcf and than can we divide with other numbers will that still work?
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
5:14 did the Y next to 30X⁴ at example 3 vanished or am i missing something
Minatwar shnkoo 😊😅❤
❤❤❤
can someone explain please, how is it negative -7x - 5x = -2x
-7x-(-5x)=-7x+5x=-2x
Who is watching from Pakistan
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?
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.