A Teacher gives the polynomial \(x^{3}-3x^{2}-4x+12\) and asks the students to factorize it. The students are expected to combine like terms and group the expression for easier factoring. The teacher rewarded the students who correctly factorized the polynomial with bonus points.
1. Which value of \(x\) is a zero of the polynomial?
2. One of the factors of the polynomial is:
3. The polynomial factorizes as:
4. The remainder when \(P(x)\) is divided by \(x-2\) is: