x^3-3x^2+3x-9=0. My book factors it to x^2(x-3)+3(x-3)=0, but then it magically becomes (x-3)(x^2+3). I have no idea how it became these numbers. Could you explain please? Thanks!

Question

x^3-3x^2+3x-9=0.  My book factors it to x^2(x-3)+3(x-3)=0, but then it magically becomes (x-3)(x^2+3).  I have no idea how it became these numbers.  Could you explain please? Thanks!

bobpursley · Answer

you have a common factor, x-3. Let me use w for it. x^2*w+3w= w(x^2+3) (x-3)(x^2+3)