Partial Fraction Decomposition: Proof of the Simplest Case: REVISITED скачать в хорошем качестве

Partial Fraction Decomposition: Proof of the Simplest Case: REVISITED

In this video I revisit my earlier video on “Partial Fraction Decomposition: Proof of the Simplest Case”,    • Partial Fraction Decomposition: Proof of t...  , because a person by the username Heliocentric brought to my attention that I had not fully completed the proof. After a few back and forth exchanges I quickly realized that indeed Heliocentric was right and I had still some part of the proof yet to be explained. The issue at hand is in the Lemma 1 part of the proof which required proving that a polynomial exists with some given characteristics. In that video though, I simply assumed that the polynomial existed and worked to prove the characteristics. This is not fully complete because I still had yet to prove that it could have been in fact a polynomial. But as Heliocentric stated, and as I promised him 6 months ago that I would complete the proof of this video “later” (i.e. finally today!), I show how the proof that the function is in fact a polynomial can be shown by the Factor Theorem. Now recall in my earlier videos that the Factor Theorem is just a special case of the Polynomial Remainder Theorem, in which the division of an univariant polynomial by (x – a) has a remainder that equals zero. This in fact is the case with the formulation in the Lemma 1, and hence the factor theorem proves that in fact there does exist a polynomial P(x) with the given characteristics. This is a very important video illustrating now only the importance of thoroughly proving each step of a derivation, but also the importance to learn from constructive feedback and always make sure to correct yourself, so make sure to watch this video! Video notes and playlist: PDF notes: https://1drv.ms/b/s!As32ynv0LoaIh44BB... HIVE notes: https://peakd.com/mathematics/@mes/pa... Partial Fractions playlist:    • Partials Fractions   Related Videos: Partial Fraction Decomposition: Proof of the Simplest Case:    • Partial Fraction Decomposition: Proof of t...   Polynomial Remainder Theorem: Factor Theorem & Factorization:    • Polynomial Remainder Theorem: Factor Theor...   Euclidean Division of Integers: Theorem and Proof:    • Euclidean Division of Integers: Theorem an...   Euclidean Division of Polynomials: Theorem and Proof:    • Euclidean Division of Polynomials: Theorem...   Polynomial Remainder Theorem: Proof + Factor Theorem:    • Polynomial Remainder Theorem: Proof + Fact...   Polynomial Remainder Theorem: Elementary Proof:    • Polynomial Remainder Theorem: Elementary P...   . ------------------------------------------------------ Become a MES Super Fan!    / @mes   DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes 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