SOLUTION: please help! can you demonstrate how to factor: 4(3-x)^2-(3-x)^3+3(3-x)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: please help! can you demonstrate how to factor: 4(3-x)^2-(3-x)^3+3(3-x)      Log On


   

Question 218103: please help!
can you demonstrate how to factor:
4(3-x)^2-(3-x)^3+3(3-x)
Answer by user_dude2008(1862) About Me  (Show Source):
You can put this solution on YOUR website!
4(3-x)^2-(3-x)^3+3(3-x)

4z^2-z^3+3z ..... I made z=3-x

-z^3+4z^2+3z

-z(z^2-4z-3)

-(3-x)((3-x)^2-4(3-x)-3) ... plugged in z=3-x

(x-3)(9-6x+x^2-12+4x-3)

(x-3)(x^2-2x-6)

Answer: 4(3-x)^2-(3-x)^3+3(3-x)=(x-3)(x^2-2x-6)