Factors and zeros greatly relate to each other. The opposite of the zero is the factor and the opposite of the factor is the zero. For example: (x-3) is a factor, the zero is 3. (x+2) is a factor, the zero is -2.
Long division or synthetic division helps factor polynomials by dividing out as much of the polynomial as possible to reduce it and make it easier to find factors and zeros.
The highest degree of a polynomial is sometimes determines how many zeros there are.
For example: y=x^2+x+1 this function has a highest degree of 2, it also has two "easy" zeros.
y=x^6+x^3+x+2 this function has a highest degree of 6, it should have and 6 zeros. This doesn't always tell us the number of factors because it depends on the multiplicity and if the equation has any repeated zeros.
Long division or synthetic division helps factor polynomials by dividing out as much of the polynomial as possible to reduce it and make it easier to find factors and zeros.
The highest degree of a polynomial is sometimes determines how many zeros there are.
For example: y=x^2+x+1 this function has a highest degree of 2, it also has two "easy" zeros.
y=x^6+x^3+x+2 this function has a highest degree of 6, it should have and 6 zeros. This doesn't always tell us the number of factors because it depends on the multiplicity and if the equation has any repeated zeros.