Question

Justify the statement all polynomials are algebric expressions but all algebric expressions are not polynomials. Give examples

Answer 1

a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables

or
A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s)

an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number

For an algebraic expression to be a polynomial,

1. It must not have a variable inside the radical symbol.
2. It must have no negative exponents.
3. No fractional exponents in the variable.

so if any algebaic expression is not satisfying above condition , it will not be polynomial

eg :
For example: x/(x+1) is an algebraic expression, but is not a polynomial as it is not defined at x = −1