Factors and zeros are connected because a zero is usually the opposite of a factor. For example if the factor is x-2 the zero would be the opposite of that so 2. Division helps us factor polynomials because you can divide out some parts of the equation and get down to the factors eventually. The degree of the polynomial helps predict the number of zeros because the highest degree of the polynomial is usually the amount of zeros. They can tell us the number of factors, sometimes but it's not always reliable. The exponent could be 4 in an equation and the number of factors could only be 2 or 3.