No one in my family can get this problem, can yahoo answerers help?

Question

Find (k³ - 3k - 2) ÷ (k - 2)

It is multiple choice, is it:
k^2 + 2k + 1
k + 2
k^2 + 2k + 1 - (4/k - 2)
or
k^2 - 2k - 7 - (16/k - 2)

Answer 1

We need to bring the numerator in a form that is divisible by k-2

K^3 - 3k - 2
Add and subtract 2k^2 to it. Also split -3k into -2k and -k
=> K^3 - 2k^2 + 2k^2 - 2k - k - 2
To this add and subtract -2k and +2k
=> K^3 - 2k^2 + 2k^2 - 4k + 2k - k - 2
collecting k - 2 from all the terms
=> k^2 (k-2) + 2k (k - 2) + (k - 2)
= (k - 2) (k^2 + 2k + 1)
=> Nr (k - 2) (k + 1) ^2
Nr/Dr = (k - 2) (k + 1) ^2 / (k - 2)
= (k + 1) ^2 = (k^2 + 2k + 1)

Your choice 1 is correct