Are there any quadratic equations that cannot be solved by factoring? Why or why not?
Yes, only certain quadratic equations are factorable. All the rest that can't be factored? You'll have to resort to another method to solve those.
The a, b, and c coefficients of the quadratic equation must have a special relationship in order for it to be broken down into easy-to-handle factors. Here's a way to check:
- get the equation into ax^{2} + bx + c = 0 form
- multiply a and c and get a product (this product is called ac)
- list all the factor pairs of ac
- if there's a factor pair that you can add or subtract together to equal the b coefficient, then the equation is factorable.