Yes, all polynomial functions are continuous.
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You can evaluate a polynomial, you can factorise a polynomial, you can solve a polynomial equation. But a polynomial is not a specific question so it cannot be answered.
An algebraic number is one that is a root to a non-zero polynomial, in one variable, whose coefficients are rational numbers.Equivalently, if the polynomial is multiplied by the LCM of the coefficients, the coefficients of the polynomial will all be integers.
monomial
The degree of a polynomial is the sum of all of the variable exponents. For example 6x^2 + 3x + 2 has a degree of 3 (2 + 1).