Determine whether the algebraic expression is a polynomial. If it is a polynomial, write the polynomial in standard form, determine the degree, and state if it is a monomial, binomial, or trinomial. $\newline$ $3 x^{-4}+6$ $\newline$ Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. $\newline$ A. The expression is a polynomial. The polynomial written in standard form is $\square$ , and the degree of the polynomial is $\square$ . $\newline$ B. The expression is not a polynomial. $\newline$ Choose the correct type of polynomial. $\newline$ A. Trinomial $\newline$ B. Monomial $\newline$ C. Binomial $\newline$ D. None of these

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Algebra 2

Factor out a monomial

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Q. Determine whether the algebraic expression is a polynomial. If it is a polynomial, write the polynomial in standard form, determine the degree, and state if it is a monomial, binomial, or trinomial.

\newline

3 x^{-4}+6

\newline

Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

\newline

A. The expression is a polynomial. The polynomial written in standard form is

\square

, and the degree of the polynomial is

\square

\newline

B. The expression is not a polynomial.

\newline

Choose the correct type of polynomial.

\newline

A. Trinomial

\newline

B. Monomial

\newline

C. Binomial

\newline

D. None of these

Check for Polynomial Criteria: To determine if an expression is a polynomial, we need to check if the expression consists of a finite number of terms, each of which is a product of a constant and a non-negative integer power of the variable. Use math mode for all numbers, variables, symbols, operators, etc. Use math mode for all orphaned numbers.
Identify Negative Exponent: The given expression is $3x^{-4} + 6$ . We notice that the term $3x^{-4}$ has a negative exponent. Polynomials cannot have negative exponents.
Conclusion: Since the expression contains a term with a negative exponent, it is not a polynomial. Therefore, we do not need to write it in standard form, determine its degree, or classify it as monomial, binomial, or trinomial.
Correct Choice: The correct choice is B. The expression is not a polynomial. We do not need to choose a type of polynomial since it is not a polynomial.