Question

what is the difference between algebraic expression and a polynomial

Answer 1

algebraic expression is made up of constant , integers and variables...
whereas a polynomial consisting only term ...

Answer 2

" Algebraic expression " is not a precisely defined term.
Algebraic expressions include many things which are not considered polynomials , including rational functions , which comes from dividing polynomials , and thing like x.
Some differences are:-
1) "Algebraic expression may not be a continous function on R , whereas polynomial is ".
2) Polynomial is a precisely a defined term .A polynomial is constructed from constants and variables by adding and multiplying.
One should add ' subtracting ' , but x- y is
x +( - 1) y, so adding and multiplying are enough.

3) " Algebraic expression" is not a precisely defined term. Algebraic expression include many many..... things that are not polynomials, including rational functions , which comes from dividing polynomials, and things like
$\sqrt{x}$

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