Final answer:
To divide a quadratic equation by another polynomial, one can use polynomial long division or synthetic division when the divisor has a lower degree than the quadratic. Factorization can help simplify the expression but is not a division method. The quadratic formula resolves the quadratic equation to find its roots but does not involve division. Option a is the correct answer.
Step-by-step explanation:
To divide a quadratic equation by another polynomial equation, we can use polynomial long division or synthetic division, given that the divisor is of lower degree than the quadratic. Long division is similar to numerical division, where we divide, multiply, subtract and then bring down the next term sequentially. Synthetic division is a shorthand method of polynomial division when the divisor is of the form x - k, and it simplifies the process by dealing only with the coefficients.
Factorization involves writing the quadratic as a product of its factors if possible, but this doesn't apply to division by another polynomial. The quadratic formula, which finds the roots of a quadratic equation in the form ax²+bx+c = 0, where a ≠ 0, is not a method of division, but rather of solving the equation to get the values of x by using the quadratic formula: x = (-b ± √(b² - 4ac))/(2a).
As an example, consider dividing the quadratic equation t² + 10t - 200 by t - 10. We can use either polynomial long division or synthetic division since the divisor t - 10 is a first-degree polynomial.