Question

Witch one is polynomial

A.)(x⁸ -2)/(x⁻² +3).
B.)1/x-1.
C.)x² +2.
D.)7x⁷ -2x⁻⁴ +3

Answer 1

Option C, x² +2, is the only expression that is a polynomial because it only contains terms with non-negative integer exponents and no variables in the denominator.

Step-by-step explanation:

To determine which of the given options is a polynomial, we need to understand the defining characteristics of a polynomial. A polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involve only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Polynomials must have whole numbers as exponents and cannot have variables in the denominator.

• An expression like (x⁸ -2)/(x⁻² +3) is not a polynomial because it has a variable (x) in the denominator.
• The expression 1/x-1 also has a variable in the denominator, so it is not a polynomial.
• The expression x² +2 is a polynomial because it only includes terms with non-negative integer exponents and there are no variables in the denominator.
• The expression 7x⁷ -2x⁻⁴ +3 includes a term with a negative exponent, which is not allowed in a polynomial.

Therefore, the correct answer is C.) x² +2 which is indeed a polynomial because it adheres to the definition of a polynomial.