# Polynomial Long Division: (x - a) is a factor of (x^k - a^k) PROOF

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In this video I go over a very interesting algebra proof and which is to show that (x – a) is a factor, i.e. divides evenly, into the function xk – ak. The derivation of this can be shown by using polynomial long division until we start noticing a pattern. Once the pattern of decreasing powers of x and increasing powers of a is revealed, we can then use it to show that eventually the remainder will be 0. Thus proving the formulation! This is a very interesting method of derivation and I will be using this proof in my later videos on algebra so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIh4Il87_E56J68Cgb4A

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/polynomial-long-division-x-a-is-a-factor-of-x-k-a-k-proof

Related Videos:

Polynomials - A Simple Explanation: http://youtu.be/IHIh7Y0kStE
Polynomial Long Division - In depth Look on why it works!: http://youtu.be/E1H584xJS_Y
Polynomial Long Division - Examples: http://youtu.be/7XbzCQgqBPc
Factoring Quadratic Polynomials by Guessing: http://youtu.be/biEfGwT5pn4
Direct Substitution for Polynomials - Simple Proof: http://youtu.be/Fnb72ERTLqY
Polynomial Long Division: Multiple Variables: http://youtu.be/vrElU5SR6Aw
Euclidean Division of Polynomials: Theorem and Proof: https://youtu.be/ONxn17okl5c
Polynomial Remainder Theorem: Proof + Factor Theorem: https://youtu.be/q4lwSBObkXc .

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