# Polynomial Remainder Theorem: Factor Theorem & Factorization

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• Published on Dec 20, 2020

In this video I go over further into the Polynomial Remainder Theorem and this time look at a special case of it, known as the Factor Theorem. Recall that the Remainder Theorem states that the remainder of a division of an univariant (single-variable) polynomial by the polynomial x – k is equal to f(a) and is a constant. A special case of this is when the remainder is equal to 0, which thus makes the polynomial x – k a factor of f(x). This means that f(k) = 0, or in other words k is a root of f(x) and x – k is a factor of f(x). This result is useful when performing factorization of polynomials in order to write them in terms of simpler, or lesser degree, polynomials. I illustrate this through a useful example as well. This is a very interesting illustration of how the factor theorem can be used to find factors of polynomials so make sure to watch this video!

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Related Videos:

Polynomial Remainder Theorem: Elementary Proof: https://youtu.be/Im0c25WbZBg
Polynomial Remainder Theorem: Proof + Factor Theorem: https://youtu.be/q4lwSBObkXc
Polynomial Long Division: (x - a) is a factor of (xk - ak) PROOF: https://youtu.be/Yp6VU3CkIEA
Euclidean Division of Polynomials: Theorem and Proof:

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 .

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