Factoring Higher Degree Polynomial Functions & Equations - Algebra 2

Sdílet
Vložit
  • 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...
    _______________________________________
    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...
    _______________________________________
    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

Komentáře • 162

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  Před 7 měsíci +2

    Factoring Formula Sheet: bit.ly/4dFNZJ8
    Final Exams and Video Playlists: www.video-tutor.net/

  • @TheQueenofNeckbeards
    @TheQueenofNeckbeards Před 5 lety +295

    I'm taking an independent Algebra 2 course and factoring has been my weakness. Bless your soul for this video.

  • @dudybug
    @dudybug Před 2 lety +53

    I’m here from a Calculus II class halfway through college. Learn your factoring, kids 😞

  • @gabesusman4592
    @gabesusman4592 Před 2 lety +44

    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

  • @shingiriraitogo4193
    @shingiriraitogo4193 Před 6 lety +28

    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.

  • @GODiKING
    @GODiKING Před rokem +7

    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

  • @pitluggreymore6504
    @pitluggreymore6504 Před 4 lety +29

    6:47 starts factoring by grouping

  • @TroyNea
    @TroyNea Před 6 lety +88

    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?

    • @ar6069
      @ar6069 Před 5 lety +4

      Alex Nwaosa Good question...i was wondering the same

    • @tomato7453
      @tomato7453 Před 5 lety +7

      @@ar6069 reduce with "x" as the gcf and factor from there

    • @0xVENx0
      @0xVENx0 Před 5 lety +2

      Yup, x^2 is very similar to x^2 almost same in factoring

    • @simplehumancomplexambition9884
      @simplehumancomplexambition9884 Před 5 lety +25

      Yea, he chose the easy-factorable equations.

    • @liliacfury
      @liliacfury Před 4 lety +3

      He has other videos explaining that

  • @rabbitwhite934
    @rabbitwhite934 Před 3 lety +4

    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!

  • @smallnoob7577
    @smallnoob7577 Před 3 lety +21

    this guy still carrying me through high school :D

  • @ventilator7914
    @ventilator7914 Před 9 měsíci +1

    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

  • @ErykKrzeminski
    @ErykKrzeminski Před rokem +3

    Thank you so much!
    These videos are just great, I can't thank you enough!

  • @mainfield4963
    @mainfield4963 Před 11 měsíci

    I am in high school though but sometimes yk you have to again remember. This helped. Thanks ❤

  • @bcuniverse_
    @bcuniverse_ Před 2 lety

    using this and the quadratic formula for higher-level eigenvalue matrices in college. Math really do go in circles

  • @cedrickbenson8825
    @cedrickbenson8825 Před 5 měsíci

    Thank you, Juliano Gonzalez❤🎉

  • @Aishwaryakaranth2507
    @Aishwaryakaranth2507 Před 4 lety +15

    Sir,what if we have odd powers instead of even ..how do we substitute??

  • @teramajtaklu2180
    @teramajtaklu2180 Před 6 lety +12

    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.

    • @louvivier7779
      @louvivier7779 Před 4 lety +3

      'Board' 'Board' 'Board' 'Board' 'Board' 'Board' 'Board' 'Board'

    • @stonewall1485
      @stonewall1485 Před 4 lety +1

      Bored*

    • @burnt_toast03
      @burnt_toast03 Před 3 lety

      Can't ya'll tell this isn't his first language? Geez people, this is the comments section, Who cares.

    • @Henok-qn6nc
      @Henok-qn6nc Před 5 měsíci +2

      @@burnt_toast03 these are unemployed spell checkers 😂😂😂

  • @aux2680
    @aux2680 Před rokem +2

    I get the basis of this, but what if you can't factor out your terms because they're different numbers?

  • @juissionhyvaa1407
    @juissionhyvaa1407 Před 7 měsíci

    YOU ARE SAVING MY LIFE I LOVE YOU SO MUCH

  • @beetdigger1975
    @beetdigger1975 Před 4 lety +8

    Can you do video on how to factor a polynomial with x^3 and with a coefficients greater than one

  • @blinkbabe3684
    @blinkbabe3684 Před 2 lety +3

    you literally explained this perfectly. thank you.

  • @healthmatters8045
    @healthmatters8045 Před 9 měsíci

    Always saving my life

  • @user-yt8wl2ig1m
    @user-yt8wl2ig1m Před rokem

    Thank you so much! This video really helped me.

  • @JamesBrodski
    @JamesBrodski Před 4 lety +3

    Wow, you're a lifesaver! Thank you so very much.

  • @julietonyekaonwu3107
    @julietonyekaonwu3107 Před rokem

    Thank you for this video JD😊

  • @ngcool4112
    @ngcool4112 Před 6 měsíci

    thank you so much brother

  • @luckymusukwa3372
    @luckymusukwa3372 Před 2 lety

    Nice explanation

  • @marcusmors8485
    @marcusmors8485 Před 2 lety +2

    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?

  • @qusairamadan7838
    @qusairamadan7838 Před 7 lety +4

    Thank you teacher for everyday-useful videos

  • @ChavoMysterio
    @ChavoMysterio Před 3 lety +1

    5x^3-10x^2+4x-8
    5x^2(x-2)+4(x-2)
    (5x^2+4)(x-2)

  • @aaron9262
    @aaron9262 Před rokem

    Hi im an asian chinese boy 11 year old this has been really easy hoiyaaaa

  • @Yashaswee_Singh
    @Yashaswee_Singh Před 5 měsíci

    Thank youu❤❤

  • @theprosusmovement3885
    @theprosusmovement3885 Před 4 lety +2

    Thank you so much for the video very simple and helped a bunch

  • @emilyjohnson2544
    @emilyjohnson2544 Před 3 lety +2

    OH MY GOSH YOU ARE SO SMART

  • @xxpurplexxrosexx
    @xxpurplexxrosexx Před 2 lety

    You're way better than my professor

  • @aheadofthegame1
    @aheadofthegame1 Před 2 lety

    Bro clutching up for the precalc quiz

  • @yvonnemwambani6205
    @yvonnemwambani6205 Před 4 lety +1

    5x^48 + 6x^10 - 5x - 6 is divided by x - 1

  • @austinchandler3079
    @austinchandler3079 Před 5 lety +2

    What would you do if you couldn't factor by grouping?

    • @gamerdio2503
      @gamerdio2503 Před 5 lety

      Synthetic division. There are plenty of tutorials online.

    • @austinchandler3079
      @austinchandler3079 Před 5 lety

      @@gamerdio2503 Thank you.

    • @gamerdio2503
      @gamerdio2503 Před 5 lety

      @@austinchandler3079 Here's a good video describing it: czcams.com/video/rP-__zFngio/video.html

  • @sacha8771
    @sacha8771 Před 6 měsíci

    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)

  • @jessejames258
    @jessejames258 Před 3 lety +8

    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

  • @lucapointcom
    @lucapointcom Před 6 lety +1

    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

  • @bobu5213
    @bobu5213 Před měsícem

    3:40 why don't you factor x^2 + 4 too?

  • @tjb19861124
    @tjb19861124 Před 6 lety +3

    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)?

  • @lumhoxha2856
    @lumhoxha2856 Před 6 lety +1

    So thanks man, you helped me so much ❤👍👍

  • @shadowkokufu9178
    @shadowkokufu9178 Před 4 lety +2

    What about the ones that you can't use grouping for??

  • @rangerrojan1283
    @rangerrojan1283 Před 2 lety

    hello, how can you answer this with perenties [ ( ) ] like this (4x-y)^4.

  • @ngocbui2928
    @ngocbui2928 Před rokem

    tksm

  • @702sundevil
    @702sundevil Před 3 lety +1

    How about 0.05x^4 + x^3 -14x+16 ? How would you factor ?

  • @tahj6277
    @tahj6277 Před 5 lety

    Thank you so much

  • @Gd_Monsterforce
    @Gd_Monsterforce Před 3 měsíci

    I’m not sure what it’s called, but I just call the method Quadratic Substitution

  • @makenzie2353
    @makenzie2353 Před 6 lety +1

    Great strategy!

  • @silvannaaurelius2217
    @silvannaaurelius2217 Před 3 lety

    How about Quintic Polynomials?with (5 terms)?

  • @cameronluster
    @cameronluster Před 2 lety

    How do you factor x^3+11x^2+10x=0

  • @nadiaseid1137
    @nadiaseid1137 Před 4 lety

    You are amazing

  • @stuffstowatch2379
    @stuffstowatch2379 Před 2 lety

    9x^4 + 3x^3 - 2x^2 + 3x - 1
    2x^4 + 3x^3 + 2x^2 + 1
    How to factor such polynomials?

    • @kkuznetsov2424
      @kkuznetsov2424 Před 2 lety

      use synthetic division. i believe the oct has already covered it

  • @laugh_345
    @laugh_345 Před 5 měsíci

    Do x⁴+x²+25

  • @shockus1154
    @shockus1154 Před 3 lety +1

    How do you factor out x^4+5x^2+9?

  • @yvonnemwambani6205
    @yvonnemwambani6205 Před 4 lety

    How can this be factorised x^12-4096

  • @alizarehan9405
    @alizarehan9405 Před 5 lety

    Can you please solve this a^4-7a^2+1

  • @gabriellemueller8848
    @gabriellemueller8848 Před 2 lety

    Hello, @ 2:12, why didn't you break down the (x2+9) into (x-3)(x+3), pls Thanks

    • @billhill6464
      @billhill6464 Před 2 lety +1

      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.

  • @craigl5054
    @craigl5054 Před 4 lety +1

    but bro for the first one can't you also say (x^2-1)(x^2+9)? it works out the same.

    • @caleb1829
      @caleb1829 Před 3 lety

      (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)

  • @Amandaks286
    @Amandaks286 Před měsícem

    2024.
    I'm doing Engineering Mathematics II on my 2nd year degree, learning factoring. Don't take school lightly.

  • @bernadettebagtas4870
    @bernadettebagtas4870 Před 3 lety +1

    3x³ + 6x² + 9x =

  • @tristiandang6236
    @tristiandang6236 Před 3 lety

    I finally filled the void form a few months of neglecting

  • @destinationahead6221
    @destinationahead6221 Před 7 měsíci

    These easy factorization won't help jee students increase ur level bro

  • @narutouzamaki3272
    @narutouzamaki3272 Před 4 lety +2

    how can i repay you

  • @sleeplessnight2713
    @sleeplessnight2713 Před 3 lety +2

    Im dying trying to understand the concept of the lesson

  • @aditiwadate5185
    @aditiwadate5185 Před 5 lety +2

    If x^5 polynomial then

  • @what7018
    @what7018 Před 2 lety +2

    I’m dying😭😭

  • @thesupremepebble3690
    @thesupremepebble3690 Před 2 lety

    I have polynomials with 6 terms. What do i DO?!??

  • @Zenosama26
    @Zenosama26 Před 6 lety

    Take this example x7+1 (x raised to 7 + 1)

  • @Youngballer739
    @Youngballer739 Před 3 lety

    What do you do when none of these rules apply?

  • @filipborin555
    @filipborin555 Před 5 lety

    Great video again hehe.

  • @jagjitsingpawar8322
    @jagjitsingpawar8322 Před 4 lety

    thank u bro that was goood

  • @moondust2365
    @moondust2365 Před 4 lety

    What do you do if the first pair isn't the same ratio as the last pair?

  • @jdlopez131
    @jdlopez131 Před 5 lety

    is there a general form to solve for higher order polynomials? like -b sqrt(b^2 - 4ac)/2a ?

    • @emomu
      @emomu Před 4 lety

      There are, but they are longer formulas. If you can't factor it, then you have to use the rational roots theorem.

  • @syonix__5799
    @syonix__5799 Před 4 lety

    What up Mrs. Jereze class

  • @tiffanyjones4241
    @tiffanyjones4241 Před 7 lety +1

    how did you go from x to a??

    • @carldaoud
      @carldaoud Před 7 lety +2

      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".

  • @ryanhsu1241
    @ryanhsu1241 Před 3 lety

    Bro I’m so fked I’m in ap calc and I can’t factor properly 😭

  • @daniah3551
    @daniah3551 Před 2 lety

    Ily

  • @nikhilnirmal7772
    @nikhilnirmal7772 Před 6 lety

    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 .

  • @mixtube2875
    @mixtube2875 Před 3 lety

    how is A²=x⁶ in 3rd example it has to be equal to x⁵

  • @jirkadolezal8127
    @jirkadolezal8127 Před rokem

    👍👍👍👍👍👍👍👍👍👍👍👍

  • @arnoldmande1707
    @arnoldmande1707 Před 6 lety

    #Knw i got it#

  • @louiseramis1529
    @louiseramis1529 Před 4 lety

    What is the " i " thing

  • @Firebird0500
    @Firebird0500 Před 3 lety +1

    Wow i can't understand stand it ಠωಠ

  • @jacquelinediaz6796
    @jacquelinediaz6796 Před 3 lety

    Still don’t understand

  • @irritspeenowhale
    @irritspeenowhale Před 7 měsíci

    Lord savior

  • @Memeer-hf5ij
    @Memeer-hf5ij Před 3 lety

    Lordt I'm so confused

  • @01utpalraj95
    @01utpalraj95 Před 4 lety

    X^8+x^4+1 factorise it plz

  • @craigl5054
    @craigl5054 Před 4 lety

    OH NEVERMIND

  • @Nin..
    @Nin.. Před 3 lety +1

    m a t h solve depression.

  • @ttatiana6299
    @ttatiana6299 Před 7 lety

    Nifty but is he crying

  • @angel1202003
    @angel1202003 Před 6 lety

    yassss

  • @LuisMartinez-ry7dk
    @LuisMartinez-ry7dk Před 4 lety

    great vid but speak up a little

  • @seanh2910
    @seanh2910 Před 4 lety

    Algebra 2 in 8th hurts

    • @pitluggreymore6504
      @pitluggreymore6504 Před 4 lety

      How you so advanced in 8th

    • @jonathanvilchez4701
      @jonathanvilchez4701 Před 4 lety +1

      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

  • @nyxdausen4552
    @nyxdausen4552 Před 3 lety

    Thank you soo much