Final answer:
The division of the polynomial given can be verified using synthetic division, and solving a quadratic equation can be done using the quadratic formula.
Step-by-step explanation:
The process of dividing polynomials can be performed using polynomial long division or synthetic division. The given expression (6x³ + x² - 31x + 10) ÷ (x - 2) seems to already be divided, resulting in 6x² + 1. To confirm this, we would perform synthetic division using the divisor (x - 2). The remainder should be zero if the division is correct. Additionally, solving quadratic equations like x² + 1.2x - 10²x - 6.0 × 10³ = 0 can be approached by using the quadratic formula, which resolves equations in the form ax² + bx + c = 0, where a, b, and c are coefficients.