Step 1: Understand what a polynomial is. A polynomial is an expression made up of terms that can include numbers, variables, and exponents.
Step 2: Identify the key characteristics of a polynomial. The exponents of the variables must be non-negative integers (like 0, 1, 2, etc.).
Step 3: Look at the expression given: 3x^2 + 2x - 1.
Step 4: Check each term in the expression. The first term is 3x^2, where the exponent is 2 (a non-negative integer). The second term is 2x, where the exponent is 1 (also a non-negative integer). The last term is -1, which can be thought of as -1x^0 (where the exponent is 0, again a non-negative integer).
Step 5: Since all terms have non-negative integer exponents, the expression 3x^2 + 2x - 1 is indeed a polynomial.
