Question

How can we express a general $n^{th}$ degree polynomial using Horner's method?

Answer 1

Express a general $n^{th}$ degree polynomial using Horner's method :

We know that a general $n^{th}$ degree polynomial can be written as,

$=a_0+a_{1}x+a_2{x}^2+a_3{x}^3+a_4{x}^4+\dots .+a_n{x}^n$

Taking $x$ common, we get, $a_0+x[a_1+x(a_2+x(a_3+\dots .+x(a_{n-1}+x{a}_n)..)\left)\right]$

Hence, we can express a general $n^{th}$ degree polynomial using Horner’s method as, $a_0+x[a_1+x(a_2+x(a_3+\dots .+x(a_{n-1}+x{a}_n)..)\left)\right]$