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.
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A trinomial is a polynomial. All trinomials are polynomials but the opposite is not true. a trinomial= three unlike terms. a polynomial= "many" unlike terms.
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.
No. Matrix addition (or subtraction) is defined only for matrices of the same dimensions.
It means that you can do any of those operations, and again get a number from the set - in this case, a polynomial. Note that if you divide a polynomial by another polynomial, you will NOT always get a polynomial, so the set of polynomials is not closed under division.