# what is the difference between polynomial function and algebraic function ?

Sunil Kumar FP
8 years ago

an algebraic function of degreenin one variablexis a function$y = f(x)$that satisfies apolynomial equation

$a_n(x)y^n+a_{n-1}(x)y^{n-1}+\cdots+a_0(x)=0$

Apolynomial functionis a function that can be defined byevaluatinga polynomial. A functionfof oneargumentis called a polynomial function if it satisfies

$f(x) = a_n x^n + a_{n-1} x^{n-1} + \cdots + a_2 x^2 + a_1 x + a_0 \,$

A polynomial is always going to be an algebraic expression, but an algebraic expression doesn't always have to be a polynomial. An algebraic expression is an expression with a variable in it, and a polynomial is an expression with multiple terms with variables in it.

Algebraic expression (not polynomial): 3b
Polynomial: 4x^2 + 3x - 7

in simple words polynomial function are subsets of algebraic function.

thanks and regards
sunil kr