PreCalcCaching Box 4 - Polynomials and Sigma help

I need the solutions to the following problems. I have worked hard on them and come up with answers but do not know how to proceed.

1. Find the product of the roots of x^5-7x^2+6x-12=0

My answer: 12.

2. When x^27 - 6x^13 -x^4 + 4 is divided by x -1, the remainder is http://mathbits.com/caching/PCmath44b2.gif. What value will fill the empty box?

My answer: -2

3. In the equation 2x^4 - 6x^2 + 4x - 3 = 0, the sum of the roots is ___.

My answer: 2 + sqrt(3)

4. If (2 - i) and sqrt(3) are two roots of x^5 - 3x^4 - 2x^3 + 14x^2 - 3x - 15 = 0, find the equation's one rational root.

My answer: -1.

Final question to move on to next page: Evaluate http://mathbits.com/caching/pcmathsum9.gif

I cannot determine an answer for this one.

Thanks in advance :)