Factoring Polynomials: x^3 - 3x^2 +6x - 18

[MickieMik]

Factor Completely x^3 - 3x^2 +6x - 18 I really don't understand problems like this. First you need to fine the GCF right, there really isn't one, so what do you do? Or do you break it up like this?

x^2(x-3) + 6(x-3) I think I just answered my own question.
Since (x-3) is common to both terms it can be factored out
(x-3)(x^2 + 6) It checks (I think) so I guess I did answer my own question but please confirm. Thanks

 

[Mrspi]

Re: Factoring Polynomials

Factor Completely x^3 - 3x^2 +6x - 18 I really don't understand problems like this. First you need to fine the GCF right, there really isn't one, so what do you do? Or do you break it up like this?

x^2(x-3) + 6(x-3) I think I just answered my own question.
Since (x-3) is common to both terms it can be factored out
(x-3)(x^2 + 6) It checks (I think) so I guess I did answer my own question but please confirm. Thanks

You can check your own work....

Do either of the factors you have break down further? Is the product of the two factors your original expression?

Good work!

 

[sgtpepper]

You can check your answer by plugging values into your final and beginning equation and making sure the end values are the same:

x^3 - 3x^2 +6x - 18 = ?

x^2(x-3) + 6(x-3) = ?

(x-3)(x^2 + 6) = ?

you can check quickly here:

http://tinyurl.com/5mbllg