Question 454099
The fastest way is simply to use the quadratic formula. The roots of the equation are


*[tex \LARGE q = \frac{52 \pm \sqrt{(-52)^2 - 4(63)(-20)}}{126}]


This simplifies to q = -2/7 or q = 10/9. Using the fact that if q is a root of a polynomial, then x-q is a factor of the polynomial, the original polynomial can be expressed as


*[tex \LARGE 63q^2 - 52q - 20 = 63(q + \frac{2}{7})(q - \frac{10}{9})]


Usually when we factor something, we want all coefficients to be integers. We can distribute the 63 over the other two factors:


*[tex \LARGE 63(q + \frac{2}{7})(q - \frac{10}{9}) = (7q + 2)(9q - 10)]