Polynomial Evaluation (Horner Form)
Polynomial Evaluation (Horner Form)
\[\begin{aligned}
P(x) &= a_0+a_1x+a_2x^2+\cdots+a_nx^n \\
P(x) &= (\cdots((a_nx+a_{n-1})x+a_{n-2})x+\cdots+a_1)x+a_0
\end{aligned}\]
Variables
P = polynomial value
x = evaluation variable
a0 = constant coefficient
a1 = linear coefficient
a2 = quadratic coefficient
a3 = cubic coefficient
a4 = quartic coefficient
Description
What is this formula?
This formula evaluates a polynomial using its coefficients and a chosen value of x. Polynomial evaluation is fundamental in algebra, numerical analysis, engineering and scientific computing.
When to use it
Use this formula when calculating the numerical value of a polynomial for a specific input variable.
Example
For:
P=2+(3*x)+(4*x²)
If x=2:
P=2+(3*2)+(4*2²)
P=2+6+16
P=24
Applications
Polynomial interpolation
Curve fitting
Engineering calculations
Scientific simulations
Computer graphics
Numerical methods
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