Consider the polynomial p(x) = x^3 + 2x + 1. (The earlier garbled symbols are corrected here for clarity.) What is the degree of this polynomial?

Introduction / Context:
The degree of a polynomial is the highest power of the variable x with a nonzero coefficient. The original text contained extraneous symbols making it non-polynomial. Under the Recovery-First Policy, we repair it to the standard polynomial p(x) = x^3 + 2x + 1 so the question remains meaningful and solvable without changing the core intent (finding degree).

Given Data / Assumptions:

• Polynomial: p(x) = x^3 + 2x + 1.
• All terms are powers of x with nonnegative integer exponents.

Concept / Approach:
Identify the term with the largest exponent of x. The exponent associated with that term is the degree. Constants have degree 0, linear terms degree 1, quadratic terms degree 2, cubic terms degree 3, and so on.

Step-by-Step Solution:

Verification / Alternative check:
No like terms combine to raise the degree; the cubic term remains dominant. Hence 3 is final.

Why Other Options Are Wrong:

• 2, 4, 5, 1: They misread the highest power or treat the corrupted original text as valid; degree is set solely by the x^3 term here.

Common Pitfalls:

• Treating non-polynomial expressions (e.g., 1/x) as part of a polynomial; polynomials cannot have negative exponents.
• Ignoring the highest-power term when constants or linear terms are present.

Final Answer:
3