In the math class, the teacher began a new lesson on polynomials. To make the class more engaging, the teacher divided the whole class into four groups. Then, the teacher gave a polynomial expression \(P(x)=3x^{3}-5x^{2}+2x-7\) and asked them a few questions related to it, such as identifying the degree,type,and behavior of the polynomial. The group that answered the questions first and correctly received appreciation and a reward from the teacher.
Based on the above situation try to find the answers for the below questions.
1. What is the degree of the polynomial \(P(x)\)?
2. What type of polynomial is \(P(x)\)?
3. Identify the leading coefficient of the polynomial?
4. If \(P(x)\) is divided by \(x-1\), the remainder is found using: