Ring theory question about polynomial rings

Let R={f(x) included in Q[x]: the coefficient of x in f(x) is 0} Prove that R is a subring of Q[x]. I know to prove a subring I need to show that there is a 1 in R (is this only to prove that it' a commutative subring with 1?), I know I also need to prove that R contains 2 elements that when subtracted are also in R, and I know that the multiplying 2 elements in R the product needs to be in R. I am at a loss as how to formally describe all this. Help please. This is for a class that is an elective, it's not even required for my degree but I really like working with the algebra and I wanted a deeper understanding to share with my senior students. Thank you for your assistance

Peter and Ray built a bike ramp

Peter and Ray built a bike ramp from 20 sheets of 4ft. X 8ft. plywood and propped it up on one end with some bricks. The finished ramp is rectangular. Show 3 ways they might have arranged the wood and give the measurment for each side. Assuming that they used every sheet of plywood, what is the total area of the ramp regardless of its shape?

Text Book: - Contemporary Abstract Algebra, Author:- Gallien

In page 424 : - Theorem 25.1( Please mention each and every step). In page 424:- Theorem 25.2 (Please mention each and every step). Page 425 : - Theorem 25.3 (Please mention each and every step). Page 426 :- Corollary 1 and Corollary 2 (Please mention each and every step). In Page 430 (EXERCISE PROBLEMS). 1, 4, 5, 9, & 16 (I request please mention each and every step) .

Text Book: - Contemporary Abstract Algebra, Author:- Gallien

In page number 430 & 431 , I need following questions to be answered 6, 7, 8, 16 & 17. Last Question:- Give examples of groups with specific properties (Simple group & Non Simple Groups) At least 10 examples. (Please refer Chapter 25).? Please mention each and every step in an understandable manner.

Text Book:- Contemporary Abstract Algebra. Author:- Gallien

In page number 449, i need following questions to be answered: 4, 12/a, b, 21, 22, 24. 25. Please mention each and ever step.