Question

Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these. $$(2/3)t6+(3/t5)+1(2/3)t^6$+(3/t^5)+1$$

Accepted Answer

First, write down the given expression clearly: $$\frac{2}{3}t$$^{6}$$ + \frac{3}{t$$^{5}$$} + 1. $$Recall that a polynomial is an expression consisting of variables raised to non-negative integer exponents, combined using addition, subtraction, and multiplication by constants. Terms with variables in the denominator or with negative exponents are not allowed in polynomials. Examine each term: The first term $$\frac{2}{3}t$$^{6}$$ is a constant multiplied by t$$^{6}$$, which is valid in a polynomial. The second term $$\frac{3}{$$t^{5}$$}$$ can be rewritten as 3t$$^{-5}$$, which has a negative exponent, so this term is not allowed in a polynomial. The third term 1$ is a constant term, which is allowed. Since the expression contains a term with a negative exponent, the entire expression is not a polynomial. Therefore, you do not need to determine the degree or classify it as monomial, binomial, or trinomial because the expression is not a polynomial.

Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these. $(2 / 3) t^{6} + (3 / t^{5}) + 1$

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Key Concepts

Definition of a Polynomial

Degree of a Polynomial

Classification by Number of Terms

Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these. (2/3)t6+(3/t5)+1(2/3)t^6+(3/t^5)+1