Factoring Higher Degree Polynomial Functions & Equations - Algebra 2
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- čas přidán 8. 09. 2024
- This algebra 2 video tutorial explains how to factor higher degree polynomial functions and polynomial equations. It shows you how to factor expressions and equations in quadratic form using substitution. It shows you how to factor cubic polynomials using the factor by grouping method and how to factor special cases such as difference of squares and sum of cubes expressions. This video contains plenty of examples and practice problems.
How To Factor Trinomials:
• Factoring Trinomials T...
The Greatest Common Factor:
• How To Factor The Grea...
Difference of Squares & Sum of Cubes:
• Factoring Binomials Wi...
Factoring Perfect Square Trinomials:
• Factoring Perfect Squa...
How To Factor By Grouping:
• Factor By Grouping Pol...
Cubic Polynomials:
• Factoring Cubic Polyno...
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Solving Quadratic Equations By Factoring:
• How To Solve Quadratic...
Quadratic Equations Completing The Square:
• How To Solve Quadratic...
How To Factor Difficult Quadratic Equations:
• How To Factor Difficul...
Hard Factoring Examples:
• Factoring Trinomials &...
Factor Completely - Multiple Variables:
• How To Factor Complete...
Factoring Higher Degree Polynomials:
• Factoring Higher Degre...
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Factoring Trinomials With Large Numbers:
• Factoring Trinomials W...
Factor Trinomials With Negative Exponents:
• How To Factor Trinomia...
Factoring - Rational Exponents:
• Factoring Algebraic Ex...
Factor Theorem and Synthetic Division:
• Factor Theorem and Syn...
Finding All The Zeros of a Polynomial:
• Finding All Zeros of a...
Real and Imaginary Solutions:
• How To Find The Real &...
_________________________________________
Factoring Formula Sheet:
bit.ly/4dFNZJ8
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections
Factoring Formula Sheet: bit.ly/4dFNZJ8
Final Exams and Video Playlists: www.video-tutor.net/
thanks
I'm taking an independent Algebra 2 course and factoring has been my weakness. Bless your soul for this video.
The Queen of Neckbeards isn’t this alg1
@@XxxDarkContinentxxX no its algebra 2 it's in the title
Hermon T you also learn this in alg1 to tho
3x³ + 6x² + 9x =
@@bernadettebagtas4870 same
I’m here from a Calculus II class halfway through college. Learn your factoring, kids 😞
😂😂😂 same
Real
Me 2
no
no
1:50 : first strategy solution(factoring by solution)
4:00 : second strategy solution
6:25 : third strategy solution
8:20 : fourth strategy(factor by grouping for four termed polynomials)
9:50 : fifth strategy solution(answer is shown on next timestamp) pt1
10:10 : fifth strategy solution(the work to get this answer shown on previous timestamp) pt2
thank you gabe SUSman (amogus)
you are a life saver indeed. have followed all your lectures, i don know how to put but really you have touched my life. thank you so much and keep the good work sir.
0:00 Factor by Substitution
2:13 Difference of Squares Method
4:05 x to the 6 powers plus 11x Cubed plus 24
6:29 Factor by Grouping
8:23 Difference of Squares
6:47 starts factoring by grouping
Niz job, But u neglected the fact that there could be several powers i.e x^6+x^5-x^4+x^3-4x^2-x ,in a situation like this what do we do?
Alex Nwaosa Good question...i was wondering the same
@@ar6069 reduce with "x" as the gcf and factor from there
Yup, x^2 is very similar to x^2 almost same in factoring
Yea, he chose the easy-factorable equations.
He has other videos explaining that
I am in senior high school. now I go back to polynomials. And bam! Reviewing the basics once again helped me understand my physics! Thanks for the vid!
this guy still carrying me through high school :D
same
same (2)
same (3)
carrying me through college lmao
I thought factoring was easy since it was pretty basic in high school, but man going to a famous university in my area made algebra as hard as calculus
Thank you so much!
These videos are just great, I can't thank you enough!
I am in high school though but sometimes yk you have to again remember. This helped. Thanks ❤
using this and the quadratic formula for higher-level eigenvalue matrices in college. Math really do go in circles
Thank you, Juliano Gonzalez❤🎉
Sir,what if we have odd powers instead of even ..how do we substitute??
did you found out
Never board of your lecture. Your channel have been so helpful. Keep the good work. I wish I pay you for all your great effort.
'Board' 'Board' 'Board' 'Board' 'Board' 'Board' 'Board' 'Board'
Bored*
Can't ya'll tell this isn't his first language? Geez people, this is the comments section, Who cares.
@@burnt_toast03 these are unemployed spell checkers 😂😂😂
I get the basis of this, but what if you can't factor out your terms because they're different numbers?
YOU ARE SAVING MY LIFE I LOVE YOU SO MUCH
Can you do video on how to factor a polynomial with x^3 and with a coefficients greater than one
you literally explained this perfectly. thank you.
Always saving my life
Thank you so much! This video really helped me.
Wow, you're a lifesaver! Thank you so very much.
Thank you for this video JD😊
thank you so much brother
Nice explanation
Thanks for the factoring by grouping method.
Once I've gotten a bad grade in a math test because I took too much time factoring by ruffini. I made a program to do it for me.
Now, my problem are rational factors. Idk how to efficiently find them. Someone has an idea?
Thank you teacher for everyday-useful videos
5x^3-10x^2+4x-8
5x^2(x-2)+4(x-2)
(5x^2+4)(x-2)
Hi im an asian chinese boy 11 year old this has been really easy hoiyaaaa
Thank youu❤❤
Thank you so much for the video very simple and helped a bunch
OH MY GOSH YOU ARE SO SMART
You're way better than my professor
Bro clutching up for the precalc quiz
5x^48 + 6x^10 - 5x - 6 is divided by x - 1
What would you do if you couldn't factor by grouping?
Synthetic division. There are plenty of tutorials online.
@@gamerdio2503 Thank you.
@@austinchandler3079 Here's a good video describing it: czcams.com/video/rP-__zFngio/video.html
for 8:17 (x-2) (5x^2+4) is not the answer as it =0 so you have to find the value of x and (5x^2+4) is X doesnt belong to ER so (x-2)=0= (x=2)
What if you get problems where the stars don't align? lol
I'm still stuck on f(x) = x^4 - x^3 - 5x^2 + 3x + 6
exactly
Im still stuck on it too..
Then do synthetic division?
Quick Question: does [A^2 + B^2 = (A + Bi)(A-Bi)]? I haven't don't much experience with imaginary numbers so correct me if I am missing something
yed
yes not yed
Yes
3:40 why don't you factor x^2 + 4 too?
why wouldn't you write out the perfect squares of the first set [(x+2)(x+2)] instead of just writing out (x+9)(x-3)?
So thanks man, you helped me so much ❤👍👍
What about the ones that you can't use grouping for??
hello, how can you answer this with perenties [ ( ) ] like this (4x-y)^4.
tksm
How about 0.05x^4 + x^3 -14x+16 ? How would you factor ?
Thank you so much
I’m not sure what it’s called, but I just call the method Quadratic Substitution
Great strategy!
How about Quintic Polynomials?with (5 terms)?
How do you factor x^3+11x^2+10x=0
You are amazing
9x^4 + 3x^3 - 2x^2 + 3x - 1
2x^4 + 3x^3 + 2x^2 + 1
How to factor such polynomials?
use synthetic division. i believe the oct has already covered it
Do x⁴+x²+25
How do you factor out x^4+5x^2+9?
How can this be factorised x^12-4096
Can you please solve this a^4-7a^2+1
Hello, @ 2:12, why didn't you break down the (x2+9) into (x-3)(x+3), pls Thanks
Because (x^2+9) is the addition of squares not the difference of squares. we would only be able to break (x^2+9) into (x-3)(x+3) if it was x^2 MINUS 9, not x^2 PLUS 9. thus, (x^2+9) is unfactorable.
but bro for the first one can't you also say (x^2-1)(x^2+9)? it works out the same.
(x^2-1) simplifies to (x+1)(x-1) by difference of squares and because the factors must be expressed in their simplest forms the expression will be (x+1)(x-1)(x^2+9)
2024.
I'm doing Engineering Mathematics II on my 2nd year degree, learning factoring. Don't take school lightly.
3x³ + 6x² + 9x =
Ano sagot dyan po
27x + 36x + 9x = 72x³?
I finally filled the void form a few months of neglecting
These easy factorization won't help jee students increase ur level bro
how can i repay you
Im dying trying to understand the concept of the lesson
If x^5 polynomial then
GCF
I’m dying😭😭
I have polynomials with 6 terms. What do i DO?!??
use mathway
;D
Take this example x7+1 (x raised to 7 + 1)
That's already factored.
What do you do when none of these rules apply?
use mathway
;D
Great video again hehe.
thank u bro that was goood
What do you do if the first pair isn't the same ratio as the last pair?
is there a general form to solve for higher order polynomials? like -b sqrt(b^2 - 4ac)/2a ?
There are, but they are longer formulas. If you can't factor it, then you have to use the rational roots theorem.
What up Mrs. Jereze class
wassup
how did you go from x to a??
A is used the for leading coefficient (so since the first X has a degree of 4 its the highest which means the number in front of it is the leading coefficient), b is used for the constant so the -9, constants tare usually the last numbers that don't have a "x".
Bro I’m so fked I’m in ap calc and I can’t factor properly 😭
Ily
y^8-36y^6+126y^4+84y^2+9=0
Please salve it sir ,and then the name of salveing method, and
this methods having books on
online that books link also .
send please answer with all
of steps .
bruh
@Nikhil Nirmal ?
how is A²=x⁶ in 3rd example it has to be equal to x⁵
👍👍👍👍👍👍👍👍👍👍👍👍
#Knw i got it#
What is the " i " thing
Wow i can't understand stand it ಠωಠ
Still don’t understand
Lord savior
Lordt I'm so confused
X^8+x^4+1 factorise it plz
OH NEVERMIND
m a t h solve depression.
math cause depression
@@viktorsalomonsson6096
ye
@@viktorsalomonsson6096
apparently this is accurate
@@Nin.. It got that bad in 3 months?
Nifty but is he crying
yassss
great vid but speak up a little
Algebra 2 in 8th hurts
How you so advanced in 8th
I'm in college it doesn't get easier. when he said sum of cubes or something like that I lost him though i have recently heard of imaginary numbers i is the square root of -1 and i^2=-1
Thank you soo much