Could you please provide any names of theorems or formulas referenced in answering the following math economics questions:

1) What is a polynomial function of degree four with roots of 1, 2, 3, and 5. Explain.

2) What is a polynomial function of degree three with roots 1, 2, 4. Explain.

3) Answer the following given the equation: Y =C +I + G where GDP (Y) = Consumption (C) + Investment (I) + Government Spending (G) and the following constraints: C = a+b (Y-T) where a must be positive number, b must be 0 or 1, and G=gY where g must be 0 or 1 :

3a) What are the endogenous variables in this function? Explain why.

3b) What is the economic interpretation of the parameter g. Explain.

3c) Step by step, how would you find the equilibrium national income?

3) What restrictions would we need to apply for a solution to exist? Explain.