What is the factor theorem?

The factor theorem helps us to find factors of polynomial equations, by substituting in number values for x to see whether the equation equals zero. For any polynomial P(x), the factor theorem would state that P(a) = 0, where (x - a) is a factor of P(x).

So, if P(x) = x² - 2x - 3, then we can test potential factors by substituting numerical values in for x. If we try x = 2 we find that P(2) = (2)² - (22) - 3 = -3. Therefore, (x - 2) is not a factor of P(x), as P(2) does not equal zero. However, if we use x = 3 we can see that P(3) = (3)² - (23) - 3 = 0. Therefore, (x - 3) is a factor of P(x), since P(3) = 0.