| dtewi said: Okay then. Using the quadratic equation is a nice way to factor. But what if I want to use the shorter way instead of all that radicaling and squaring and dividing. Factoring it straight into a binomial. |
Well, other option is to use Gauss' theorem (in a polynomial of integer coefficients, if there's a rational root, then the numerator divides the independent coefficient (the last one) and the denominator divides the principal coefficient (the first one)) so if you find a quick root, you can divide the polynomial by x-root and quickly factorize it. But I think that takes more time, and it's not guaranteed to get you an answer (if there are no rational roots, Gauss' theorem doesn't do jack). The utility of it is when the polynomial is of grade 3 or higher, since in grade 2 the quadratic equation always work.
Of course, there are more rules, but they only work on some polynomials, like a perfect trinomial (x^2+2x+1) can be factored easily into (x+1)^2, and some I don't remmeber. But when you grow up and learn more math, you only keep what's really useful, therefore the only factorization methods I remember are the quadratic equation and Gauss' theorem
