 So let's take a look at two important examples of factoring quadratics. So the first of our important examples is x squared minus 3x minus 6. So we start off by finding the numbers that multiply to negative 6. And we'll go through our list. We try 1 and negative 6. Nope. We try 2 and negative 3. We'll try negative 1 and 6. And since negative 2 and 3 is the last possibility, it's got to work. Nope. And here's the important thing. We've tried all of the possible factorizations and none of them worked. So this means x squared minus 3x minus 6 is not factorable. And this leads to an important idea. Not all quadratics can be factored, but you won't know that until you try every possibility. How about something like this? Well, so far we've been looking at monic polynomials where our leading coefficient is 1 and here our leading coefficient is not 1, it's 6. So what can we do now? Well, the first thing to notice is all the terms have a factor of 6. 6x squared is 6 times x squared minus 6x is minus 6 times x and a useful rule in factoring is to always remove common factors first. Since all our terms have a factor of 6, we can remove that common factor and get and this leaves us with a monic polynomial. So now we can try and factor. We need two numbers that multiply to minus 6 and the possibilities are since the factors will add to give us a negative x. We know that the negative factor must be greater than the positive factor. So we'll start by testing 1 and negative 6. How about 2 and negative 3? And that produces our factorization.