Polynomial Curve Fitting, Matrices

I've done over 50 problems for a Linear Algebra class tonight and I'm sooo burnt out. I'm giving up on these ones.. if you can help me, that would be wonderful. Otherwise, I'm turning in what I have. Strangely enough, it's the odd problems that I already have solutions to that I don't understand. Got the even ones already.

**11)** In the "Polynomial Curve Fitting" section:

The graph of a cubic polynomial function has horizontal tangents at (1, -2) and (-1,2). Find an equation for the cubic and sketch its graph.

Somehow the answer is p(x) = -3x + x^3. Just want to know the steps.

**29)** Use a system of equations to write the partial fraction decomposition of the rational expression. Then solve the system using matrices.

And the final answer should be:

**47)** Consider the matrix..

If A is the augmented matrix of a system of linear equations, find the value(s) of k such that the system is consistent.

(Answer is all real k not equal to -4/3. Just want to know how they got this so I understand it.

**58)** True or false: Every matrix has a unique reduced row-echelon form.

Thank you in advance. I appreciate it.