Explanation:

A polynomial is an algebraic expression consisting of one or more terms combined using addition, subtraction, and multiplication, where each term is a product of a constant and one or more variables raised to non-negative integer exponents.

Let's analyze each option to determine if it is a polynomial or not:

a) x^2 - x + 1:
This expression is a polynomial because it consists of three terms: x^2, -x, and 1. Each term is a product of a constant (1) and a variable raised to a non-negative integer exponent (x^2 and x). Therefore, option 'a' is a polynomial.

b) x^2 + x - 2:
This expression is also a polynomial because it consists of three terms: x^2, x, and -2. Each term is a product of a constant (1 or -2) and a variable raised to a non-negative integer exponent (x^2 and x). Therefore, option 'b' is a polynomial.

c) x^3 - x^3 + 1:
This expression is a polynomial because it consists of three terms: x^3, -x^3, and 1. Each term is a product of a constant (1) and a variable raised to a non-negative integer exponent (x^3). Therefore, option 'c' is a polynomial.

d) x^4 - x - 3:
This expression is a polynomial because it consists of three terms: x^4, -x, and -3. Each term is a product of a constant (1 or -3) and a variable raised to a non-negative integer exponent (x^4 and x). Therefore, option 'd' is a polynomial.

Therefore, the correct answer is option 'B' (x^2 + x - 2) is not a polynomial.

Correct option is option B