Question

determine if the following expression is a polynomial.

\\-5x^{-3} + 4x^5 - 3\\

yes
no

Explanation:

Analyze the definition of a polynomial

$$ \text{A polynomial is an expression consisting of variables and coefficients, where exponents of variables must be non-negative integers.} $$

Check the exponents of the given expression

$$ -5x^{-3} + 4x^5 - 3 $$

$$ \text{Exponents: } -3, 5, 0 $$

Determine if the expression is a polynomial

$$ -3 otin \{0, 1, 2, 3, \dots\} \implies \text{Not a polynomial} $$

Answer:

• Yes
• No (Correct answer)