how do you factorize -x^4+3x^3+x^2-3x
Ler's start by taking out any greatest common factor. We could choose to take out an x or a -x. I'm going to do it the second way, because it makes any potential further factoring easier. So we have...
-x(x^3 - 3X^2 - x +3) Notice, that because I took out an "-x," the signs in the parenthesis "reverse."
Let's see if we can factor the stuff in the parenthesis by "grouping." We have..
x^2(x - 3) -1(x -3)....That's good....Now, take out the greatest common factor between these terms, (x-3), and write back what we have left...This gives
(x-3) (x^2 - 1) Note that the second term is just a difference of two squares that we can further factor as (x-1) (x+1)
So, the stuff in the parenthesis factors as (x-3) (x-1) (x+1)
Now, putting everything together gives us....
-x[(x-3) (x-1) (x + 1)]
Note, some people might place the " - " in front of the leading "x" back inside the parenthesis. But, since the point of factoring is to usually find the "zeroes" of some polynomial by setting each factor to zero, it doesn't really matter. The " - " (which really represents " -1 ') would be divided away, anyway, during such a process.
Hope that helped........
