In their example of 1111, this binary representation means 2^3 + 2^2 + 2^1 + 2^0. So plugging in 2 to the polynomial x^3 + x^2 + x + 1 gives you the original va

In their example of 1111, this binary representation means 2^3 + 2^2 + 2^1 + 2^0. So plugging in 2 to the polynomial x^3 + x^2 + x + 1 gives you the original value. If the polynomial is factored, plugging 2 in still gives you the same value, but now you have at least 2 integers that multiply to give you the original value, so you've found a factor.