Final answer:
Option 2) 3x^2 - 5x is the quadratic binomial because it is in the form ax^2 + bx, where a and b are constants.
Step-by-step explanation:
The question asks which expression is a quadratic binomial. A quadratic binomial is of the form ax2 + bx, where a and b are constants. Reviewing the options: 1) 2x + 3 is linear, not quadratic; 2) 3x2 - 5x is a quadratic binomial; 3) 4x2 + 2x + 1 is a quadratic trinomial; 4) 5x3 + 2x2 includes a cubic term, so it's not a quadratic expression. Therefore, the quadratic binomial from the options provided is 3x2 - 5x.