Using the Factor Theorem (effectively)

In the last few days we've been working on a way to factor large polynomial functions (finding their zeroes) without having to guess and check and then divide.

The remainder theroem lets us determine the remainder of a division without dividing. We substitute the zero of the divisor (the value of the binomial we want to check as a factor which makes the binomial equal to zero) into the polynomial. The value of the polynomial is the remainder of the division.

The factor theroem is an extension of this idea simply because if we happen to find a value that makes the function produce a zero remainder, we know that the binomial whose zero is that value, is a factor of the polynomial.

Take a look at the examples in your module (they are particularly good for this one). The link above will take you to today's notes where we discussed how to move from guess and check, to a more efficient way of guessing at zeroes of these elusive polynomial functions.