# Polynomial evaluation

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# Introduction

It is often useful to evaluate a polynomial at a given point. The method shown below allows to calculate it by using only multiplication and addition, without any power.

# Horner's method

Only 1-degree polynomial are evaluated, e.g. 3.x^2 + 2.x + 1, can be written, by means of an astute factorization, ((3.x +2).x + 1).

```program PolyTest;

type
// coef's rank = it's degree
TDegres = 0..10;
TPolynome = record
Deg: TDegres;
Coefs: array[TDegres] of Double;
end;

function PolyEval(const aPoly: TPolynome; X: Double): Double;
var
i: TDegres;
begin
with aPoly do
begin
Result := 0;
for i := Deg downto Low(Coefs) do
Result := Result * X + Coefs[i];
end;
End;

(* Exemples *)
var
P: TPolynome;
begin
P.Deg := 2;
P.Coefs := 3;
P.Coefs := 2;
P.Coefs := 1;
WriteLn('P(',7,') = ', PolyEval(7):10:2);

P.Deg := 0;
P.Coefs := 0;
P.Coefs := 0;
P.Coefs := 1;
WriteLn('P(',7,') = ', PolyEval(7):10:2);
End
```