Question

Which of the following is a polynomial?

a) x + 2
b) x^2
c) 7x - 2x^4 + 3
d) (x^8 - 2)/(x^2 + 3)

Answer 1

Option a) x + 2 and option b) x^2 are polynomials. Option c) 7x - 2x^4 + 3 is also a polynomial. Option d) (x^8 - 2)/(x^2 + 3) is not a polynomial.

Step-by-step explanation:

A polynomial is an algebraic expression that consists of variables and coefficients, combined using addition, subtraction, and multiplication. Option a) x + 2 is a polynomial because it is a linear expression with a variable (x) and a constant term (2). Option b) x^2 is also a polynomial because it is a quadratic expression with a variable (x) raised to a non-negative integer exponent (2). Option c) 7x - 2x^4 + 3 is a polynomial because it is a sum of monomials, where each term has a variable raised to a non-negative integer exponent multiplied by a coefficient. Option d) (x^8 - 2)/(x^2 + 3) is not a polynomial because it includes a term with a negative exponent (x^4) and division by a variable term (x^2 + 3).