Nested Scheme (Help, I need a definition/explanation)

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Nested scheme, also known as Horner's scheme, is an efficient method for evaluating polynomials. It rewrites a polynomial in a nested form to minimize the number of multiplications and additions required. For instance, the polynomial f(x) = 2x^3 - 6x^2 + 2x - 1 can be expressed as f(x) = x(x(2x - 6) + 2) - 1. This technique is particularly useful for simplifying calculations in numerical methods. Understanding this method is essential for grasping more advanced topics in polynomial evaluation.
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Hi, I'm reading about polynomials and I've encountered a method called nested scheme.
The tragedy is that my math book usually has no rigorous definitions and sometimes lacks definitions.
My book is only stating that nested scheme is a method for evaluating polynomials, and thereafter it continues with two examples. It does not provide an explanation.

I cannot find any proper link, for nested scheme, in google. Can you teach me the very basics, and that should be sufficient for the understanding of more advanced topics...
Thanks for help...
 
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This sounds like something that is called Horner scheme, a technique for evaluating polynomials efficiently.

For example, f(x) = 2x3 - 6x2 + 2x - 1 can be rewritten as f(x) = x(x(2x - 6) + 2) - 1.

More information here - http://en.wikipedia.org/wiki/Horner_scheme
 
Thanks...
 

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