Explain one of the theorems that you would use to find the zero of higher degree polynomial

Rational Root Theorem:

If the rational number  is a zero of a higher degree polynomial:

where all the coefficients are integers. Then will be a factor of and will be a factor of

1. Use the rational root theorem to enumerate all possible rational zeroes of the polynomial

2. Evaluate the polynomial from the first step until you can find a zero. Let’s suppose the zero is . It will be a zero if . Then if this is true, write the polynomial as:

3. Repeat this process using this time rather than . The process finishes until we reach a second degree polynomial, then solve as it is widely known for a quadratic equation.