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A polynomial is an expression of various exponentials of a variable wich may or may nor have coefficients and constants. The coefficients may have a radical, square root, cube root etc, but not the variable.

A radical expression is any expression involving square roots, cube roots, etc. These may have the variable inside the radical but do not have to have them.

sq root (5) is a radical expression, so is sq root (x)

3x2 + 2x - 9 is a polynomial, so is x + sq root (5)

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Q: What is the difference between a polynomial and radical expression?
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