Some help on Algebra II greatly appreciated?

We're working with polynomials and I am flabbergasted. I would greatly appreciate some assistance.

1. Please find the rational roots of x^4+8x^3+7x^2-40x-60 = 0
2. Please use the rational root theorem theorem to list all possible rational roots of the polynomial equation: x^3-x^2+7x-5=0. (Do not find the actual roots.)
3. Find all zeros of the equation: 32x^2-144 = -x^4
4. Please write the polynomial equation (-3, 0), (1, 0), (4, 0).
5. RESPONDED... What is a cubic polynomial function in standard form with zeros -2, -4, and -3. Response: 3x-12? Is this a possible solution?

I hope someone can provide some guidance with these problems, I am struggling in this topic a bit.
I will reward 10 points for an answer. Thank you!

1. There's a theorem called the Rational Roots Theorem. It says that any such root has to be of the form +-p/q where p is a factor of the constant term (60) and q is a factor of the leading coefficient (1). So you have to write down all the possible rational roots of that form, and then try them one at a time.

"Try them" means plug them in and see if you get 0. Unfortunately, 60 has a lot of factors, so you have a lot of numbers to try: +-1, +-2, +-3, +-4, +-5, +-6, etc. However, you've probably learned polynomial division, so as soon as you find one root r, you know there's a factor (x - r). You can divide out that factor to get a smaller polynomial. Once you've found 2, you are left with a quadratic and you don't need trial and error anymore.

2. I just answered how to do that. See above.

3. If you write it in standard form, x^4 + 32x^2 - 144 = 0, you can replace x^2 by y. Then you'll notice it's a quadratic: y^2 + 32y - 144 = 0. Solve that the way you would any quadratic. You might get two solutions for y. For each, x^2 = y so that tells you x.

4. Very easy. Draw these points on a graph. Notice what the shape is. What is the equation for that shape?