Yes
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No. by definition, the polynomial should contain an integer as exponent and square root 1/2 is not an integer.
That's a polynomial expression.
No. A matrix polynomial is an algebraic expression in which the variable is a matrix. A polynomial matrix is a matrix in which each element is a polynomial.
Evaluating a polynomial is finding the value of the polynomial for a given value of the variable, usually denoted by x. Solving a polynomial equation is finding the value of the variable, x, for which the polynomial equation is true.
It will be a cubic polynomial.