A fruit vendor uses a formula to calculate the daily profit from selling fruit, given by the polynomial \(f(x)\) \(=\) \(x^{3}-4x+3\), where \(x\) is the price per fruit and \(f(x)\) is the profit.One day, the vendor tries selling the fruit at \(Rs.50\) per fruit and wants to quickly check if that price gives zero profit. Instead of calculating the whole expression, the vendor uses the factor theorem.
1. Examine whether \(x+2\) is a factor of \(f(x)\).
2. The remainder when \(f(x)\) is divided by \(x-1\) is:
3. If the remainder is \(0\), then \(x-1\) is:
4. If \(f(2)\) \(=0\), then \(x-2\) is: