# Factorising Cubics

#### theleontan

I have asked way too many questions, and Im really sorry if I have bothered you lot too much, but thanks so much for the help I do apprieceate every single comment, and it is a great help to my studies. (Worried)

Just a question regarding cubics, I need to factorise
x^3-kx^2+2kx-k-1, I already know x-1 is a factor. If I want to factorise this via the "long division method" how do you go about in doing that? I'm just confused with all these pronumerals, thanks for the help.

#### Prove It

MHF Helper
Let's call this function $$\displaystyle \displaystyle P(x) = x^3 - kx^2 + 2kx - k - 1 = 0$$.

You can start by evaluating $$\displaystyle \displaystyle k$$. Since you know $$\displaystyle \displaystyle x - 1$$ is a factor, that means $$\displaystyle \displaystyle P(1) = 0$$.

theleontan

#### theleontan

What do you necesarily mean by evaluating k?

#### Prove It

MHF Helper
Finding out what value k equals...

theleontan

#### theleontan

Oh, I am such an idiot . Its the case of rewriting the equation and solving for k correct?

#### Prove It

MHF Helper
Yes, once you have substituted x = 1 and noted that this is a value that makes the entire polynomial = 0.

theleontan

#### theleontan

Yeah, I have subbed x=1 one in, and ended up with 0. Now that I know x-1 is a factor do I go ahead with the long division?

#### Prove It

MHF Helper
Oops, I didn't realise that substituting x = 1 just gives 0 = 0. You can't evaluate k this way.

When you are doing the long division, you need to treat -k-1 as a single term, and remember that since x-1 is a factor, the remainder will be 0.

#### skoker

\left[ \right] you should try the " "long division method" " on this expression and post you work so we can help.