Final answer:
The question concerns factoring quadratic equations, a mathematical process for breaking down the equation into product factors. Specifically, we're looking for factors of quadratic expressions that resemble (x - p)(x - q). The mention of the quadratic formula provides a way to find solutions to a general quadratic equation, but seems unrelated to the immediate factoring task.
Step-by-step explanation:
The question given involves factoring quadratic equations, which is a mathematical process to express the equation as the product of its factors. The quadratic expressions provided, such as x^2 - 12x + 32 and x^2 - 14x + 48, must be factored if possible into the form (x - p)(x - q), where p and q are the solutions of the equation when set equal to zero. When the quadratic formula is mentioned, it refers to the formula used to find the solutions of a quadratic equation of the form at^2 + bt + c, which is typically stated as t = (-b ± √(b^2 - 4ac))/(2a).
However, there seems to be an inconsistency in the question as there's a mention of the quadratic formula with specific constants (a = 4.90, b = 14.3, c = -20.0), which don't match the provided expressions. To factor a quadratic equation, one looks for two numbers that multiply to the constant term and add up to the coefficient of the middle term. For example, for the expression x^2 - 12x + 32, we look for factors of 32 that add up to -12, which are -8 and -4, meaning the factored form is (x - 8)(x - 4).