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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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Polynomial Remainder Theorem: Factor Theorem and Factorization
Recall that the polynomial remainder theorem states that the remainder of the division of a univariant polynomial f(x) by the polynomial x - k is equal to f(k).
https://en.wikipedia.org/wiki/Factor_theorem
Retrieved: 23 September 2017
Archive: https://archive.is/tuSUBFactor theorem
In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem.[1]
The factor theorem states that a polynomial f(x) has a factor (x - k) if and only if f(k) = 0 (i.e. k is a root).[2]
Factorization of polynomials
Main article: Factorization of polynomialsTwo problems where the factor theorem is commonly applied are those of factoring a polynomial and finding the roots of a polynomial equation; it is a direct consequence of the theorem that these problems are essentially equivalent.
The factor theorem is also used to remove known zeros from a polynomial while leaving all unknown zeros intact, thus producing a lower degree polynomial whose zeros may be easier to find.
Good post and very interesting...
thanks for sharing ... i am very interested in this video because i am also a math teacher ... so this video is very useful for me ...
Sweet, glad my post helps! :)
I like your videos. They are well explained. Thanx for posting.
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