Since that is to be true for all x, we can equate the same coefficients on both sides: we must have , , and . Obviously the last equation tells us that . Putting that into the second equation, so . Putting those values into the first equation, so .
Another way to find those numbers is to use the fact that is true for all values of x. If we set x= 0 we get as before. If we set x= 1, we get . If we set x= -1, we get
Now you know that so