Here are my ideas for the questions...

In question 1, expanding we get

So we have

...[1]

...[2]

...[3]

From [2],

Then from [1]

And from [2]

For question 2,

If you factor you get

Then by the factor theorem...

and

You should be able to solve either for k...

Haha! My calculator got k = 7 after a very... long time. And I had to resort to iteration. Surely there is a more efficient way to do this.