Factors and zeros are very similar because knowing the zeros will let you know the factors and knowing the factors will let you know the zeros. The highest degree of the polynomial will tell you the number of zeros you're going to have. For example if the highest degree is 4 then the number of zeros will be 4. No because if the factor is squared it will only count as one factor but it can be two zeros.
above is an example of my work showing that the degree is 4 and the number of zeros is 4 but there are only 3 factors.
Example of how zeros and factors are basically opposite. Make the factors equal to zero and solve. You will find your zeros.