Final answer:
The correct factored form of the quadratic equation 2x^2-25x+63 is (x-9)(2x-7), which corresponds to option a.
Step-by-step explanation:
The factored form of the quadratic equation 2x^2-25x+63 is found by looking for two numbers that multiply to (2)(63) or 126 and add up to -25. The pair of numbers that fit this requirement is -9 and -14, because (-9)(-14) = 126 and (-9) + (-14) = -25.
Thus, the factored form of the equation can be written as:
(x - number1)(2x - number2)
Substituting the numbers we found, the factored form is:
(x - 9)(2x - 7)
Therefore, option a is the correct factored form of the quadratic equation.