Factor Theorem

The Factor Theorem states that for a polynomial, if plugging a number into the polynomial results in zero, then that number makes the polynomial zero at that point, and the polynomial can be divided evenly by a linear factor corresponding to that number. Conversely, if the polynomial is divisible by a linear factor, then plugging that root into the polynomial yields zero. Essentially, it links the roots of the polynomial to its factors, helping us understand and find solutions more efficiently by testing potential roots and factoring the polynomial accordingly.