Final answer:
The expression -d⁵+4d³+c√{3} is not a polynomial because it includes a square root term, which means it has an exponent that is not a whole number, disqualifying it from being a polynomial.
Step-by-step explanation:
To determine if the expression -d⁵ + 4d³ + c√{3} is a polynomial or not, we need to look at the characteristics of polynomials. A polynomial must consist solely of terms that are non-negative integer powers of the variable. The given expression does indeed include non-negative powers of d (d⁵ and d³), but it also includes c√{3}, which is a term with a square root.
Because of the square root, the expression is not considered a polynomial. Polynomials must have whole numbers as exponents, and square roots are equivalent to an exponent of one-half, disqualifying the expression from being a polynomial.
The expression -d⁵+4d³+c√{3} is a polynomial. A polynomial is an algebraic expression that involves variables, coefficients, and exponents. In this expression, the variables are d and c, the coefficients are -1, 4, and 1, and the exponents are 5, 3, and 1/2. Since all the terms in the expression are a combination of variables raised to non-negative integer powers, it satisfies the definition of a polynomial.