If you know the factors for the polynomial, you set them equal to zero and solve for x. Division helps find the zeros that aren't easily found on the graph.The degree of the polynomial helps determine the number of zeros because if it is x⁴ for example, then there will be four zeros. This also determines the number of factors because the prime factors for x⁴ are x*x*x*x, so there have to be at least four factors to be able to get to x⁴.