Polynomial Remainder Theorem: Proof + Factor Theorem

2

  • 17
  • 0
  • 0.264
  • Reply

  • Download Download Torrent Open in the desktop app ADD TO PLAYLIST

    mes

    Published on Dec 27, 2020
    About :

    In this video I go over a special case of Euclidean Division known as the Polynomial Remainder Theorem. This theorem states that the if a polynomial f(x) is divided by the linear polynomial x – a, where a is a constant, then the remainder is equal to f(a). The derivation of this theorem is actually quite simple when invoking the Euclidean Division Theorem for Polynomials, which I covered in my last video. Recall that the Euclidean Division states that for the division of two polynomials f(x)/b(x), there are two polynomials q and r such that: f(x) = b(x)q(x) + r(x) where the degree of r is less than the degree of b (or if r(x) = 0). Thus we can simply let b(x) = (x – a) which clearly shows that f(a) = (a – a) * q + r = r(x). Thus we have proved the theorem.

    Also in this video I go over some other useful insights into this theorem such as the case when the remainder, r, is equal to 0, which thus makes (x – a) a divisor or factor of f(x). This makes it useful in simplifying polynomial division and is the basis of the Factor Theorem. The Factor Theorem states that the linear polynomial (x – a) is a factor of the polynomial f(x) if and only if f(a) = 0. I may elaborate further into this theorem so stay tuned (and let me know if I should)!

    I also go over a simple example to illustrate the Polynomial Remainder Theorem. This is a very interesting application of the Euclidean Division Theorem and is useful in computational methods of long division so make sure to watch this video!

    Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIh4ElG5XEOZkYZP2tzw

    View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/polynomial-remainder-theorem-proof-factor-theorem

    Related Videos:

    Euclidean Division of Polynomials: Theorem and Proof: https://youtu.be/ONxn17okl5c
    Euclidean Division of Integers: Theorem and Proof: https://youtu.be/66juubotzi0
    Types of Numbers: Natural, Integers, Rational, Irrational, and Real Numbers: http://youtu.be/U22Z1q_Ibqg
    Long Division by Hand - An in depth look: http://youtu.be/giBZg5Vqryo
    Polynomial Long Division - In depth Look on why it works!: http://youtu.be/E1H584xJS_Y .


    SUBSCRIBE via EMAIL: https://mes.fm/subscribe

    DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

    Like, Subscribe, Favorite, and Comment Below!

    Follow us on:

    MES Truth: https://mes.fm/truth
    Official Website: https://MES.fm
    Hive: https://peakd.com/@mes
    Gab: https://gab.ai/matheasysolutions
    Minds: https://minds.com/matheasysolutions
    Twitter: https://twitter.com/MathEasySolns
    Facebook: https://fb.com/MathEasySolutions
    LinkedIn: https://mes.fm/linkedin
    Pinterest: https://pinterest.com/MathEasySolns
    Instagram: https://instagram.com/MathEasySolutions
    Email me: contact@mes.fm

    Free Calculators: https://mes.fm/calculators

    BMI Calculator: https://bmicalculator.mes.fm
    Grade Calculator: https://gradecalculator.mes.fm
    Mortgage Calculator: https://mortgagecalculator.mes.fm
    Percentage Calculator: https://percentagecalculator.mes.fm

    Free Online Tools: https://mes.fm/tools

    iPhone and Android Apps: https://mes.fm/mobile-apps

    Tags :

    mathematics calculus science math messcience

    Woo! This creator can upvote comments using 3speak's stake today because they are a top performing creator! Leave a quality comment relating to their content and you could receive an upvote worth at least a dollar.

    Their limit for today is $0!
    Comments:
    Time until mes can give away $0 to their commenters.
    0 Days 0 Hours 0 Minutes 0 Seconds
    Reply:

    To comment on this video please connect a HIVE account to your profile: Connect HIVE Account

    More Videos

    02:11
    55 views a year ago $
    00:08
    15 views a year ago $
    13:15
    8 views 3 weeks ago $
    35:57
    16 views a year ago $