Factor Theorem (x-r) is a factor of the polynomial expression that defines the function P if and only if r is a solution of P(x) = 0, that is, if and only if P(r) = 0. In other words: – Set x-r = 0 – Solve for x. x = r – Plug this r in for every x in the original polynomial – Simplify – If you get 0 then (x – r) IS a factor of the polynomial
Let’s look at how to do this using the example: In order to use synthetic division these two things must happen: There must be a coefficient for every possible power of the variable. The divisor must have a leading coefficient of 1. #1#2
Step #1: Write the terms of the polynomial so the degrees are in descending order.
Step #2: Write the constant a of the divisor x- a to the left and write down the coefficients.