1. ## Factorising Cubics

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.

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.

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

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

3. What do you necesarily mean by evaluating k?

4. Finding out what value k equals...

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

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

7. 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?

8. 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.

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