This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# HornerForm

 HornerForm[poly] puts the polynomial poly in Horner form. HornerForm puts poly in Horner form with respect to the variable or variable list vars. HornerForm puts the rational function in Horner form by nesting and . HornerForm puts in Horner form using the variables or variable lists and for and , respectively.
• When variables are not specified, HornerForm puts the polynomial or rational function into Horner form with respect to the variables identified using Variables.
Horner form of a polynomial in x:
Put a polynomial into Horner form with respect to a given variable:
Horner form of a rational function:
Horner form of a polynomial in x:
 Out[1]=

Put a polynomial into Horner form with respect to a given variable:
 Out[1]=

Horner form of a rational function:
 Out[1]=
 Scope   (2)
Order a bivariate polynomial with respect to x then y:
With respect to y then x:
Construct a rational function in two variables:
Convert the function to Horner form:
Convert to Horner form using y before x in the numerator:
An expression with rational exponents:
 Applications   (1)
Improve speed and stability for numeric evaluation of large polynomials:
Horner form of a rational function is the ratio of Horner forms:
Obtained as a ratio of Horner forms:
HornerForm recursively factors out powers of variables:
Collect groups based on powers of variables:
Factor gives the factored form:
Exponents must be integers or rationals:
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