Which of the following represents a quadratic trinomial?

A quadratic trinomial is a polynomial of the form ax² + bx + c, where a, b, and c are constants, and the term ax² indicates that it is a quadratic expression.

The first choice, x² + 2x + 1, fits this definition perfectly. It has three terms: x² (the quadratic term), 2x (the linear term), and 1 (the constant term). Since it includes a squared variable and two additional terms, it is classified as a trinomial.

The other options do not meet the criteria for a quadratic trinomial. The second choice, x + bx + c, does not contain a squared term (x²), making it a linear expression rather than a quadratic one. The third choice, 4ab + 2a + b², features a term b² but does not contain a variable squared in the form of x², and thus can't be considered a quadratic in the context of a single variable. Finally, the fourth choice, 3x + 2, is a linear polynomial since it lacks a squared term as well.

Thus, the choice that accurately represents a quadratic trinomial is the first one, x² + 2x +