Originally posted by myself on a different blog, April 2014.
Have you ever heard of synthetic division? It is a way of dividing polynomials. It is commonly taught in the chapter of college algebra or intermediate algebra pertaining to rational expressions or finding zeroes of polynomials.
The "myth" is that it can only be used when dividing by (x-#) or (x+#). Theoretically, it should be possible because synthetic division has the same coefficients in the steps as long division (look at the concept video below). Some or practically all textbooks show only how to do it with (x-#). I have never seen a textbook where the divisor has a degree larger than one. The truth is you can use synthetic division to divide by any polynomial. The degree of the dividend must be more than or equal to the degree of the divisor.
On how to do this, here is an article by Lianghuo Fan (2003):
http://eprints.soton.ac.uk/168861/1/FLH_article_on_polynomial_division.pdf
You can watch my videos on how to do synthetic division in other topics:
algebra- synthetic division - concept 1 - compares long division with synthetic division
algebra- synthetic division - example 1 - polynomial divided by (Ax+B)
algebra- synthetic division - example 2 - polynomial divided by (Ax+B) and the result has remainder
algebra- synthetic division - example 3 - polynomial divided by a binomial (degree of 2)
algebra- synthetic division - example 4 - polynomial divided by a trinomial
Obviously, they're going to look slightly different from the normal that synthetic division is done. Happy dividing.
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