Short Math Explanation
The zero of a polynomial is the point where the polynomial crosses the x-axis. Multiple zeros mean that the function crosses the x-axis more than once. Imaginary zeros come into play when you graph a quadratic equation and it does not intersect the x-axis, then it has imaginary zeros. In order to find the zeros within the polynomial you have to put the polynomial in descending order of exponents. After this is done, you use the formula (factor of a constant term a0 factor of the leading coefficient an). Then, you find all possible rational zeros by pairing the factors of q with each of the p factors. Once you have found all of the possible rational zeros, you move on to finding all of the real zeros. To find all of the real zeros, you have to choose one zero and divide the polynomial by the possible zero using synthetic division. Once you have used synthetic division, your remainder should come out to be zero. However, if your remainder is not zero, the zero we used does not work therefore it is not a rational zero. You then continue testing the zeros until you have found one that has a remainder of zero. Once you have found one that has a remainder of zero, you take that answer you set it up in factored form. The number that is next to your remainder is the constant and the next one has a power of one and so on. After this, you expand this form as far as possible. The amount of zeros you end up with will be the number of parenthetical citations. To find the zeros, you make each parenthesis equal to zero and then solve. Here you use the zero product property. The zero product property states that anything times a zero is zero. In a polynomial function there are also local minimums and maximums. A local maximum is when the graph changes from increasing to decreasing. A local minimum is when the graph changes from decreasing to increasing. The slope at the local minimums and maximums is zero.
The zero of a polynomial is the point where the polynomial crosses the x-axis. Multiple zeros mean that the function crosses the x-axis more than once. Imaginary zeros come into play when you graph a quadratic equation and it does not intersect the x-axis, then it has imaginary zeros. In order to find the zeros within the polynomial you have to put the polynomial in descending order of exponents. After this is done, you use the formula (factor of a constant term a0 factor of the leading coefficient an). Then, you find all possible rational zeros by pairing the factors of q with each of the p factors. Once you have found all of the possible rational zeros, you move on to finding all of the real zeros. To find all of the real zeros, you have to choose one zero and divide the polynomial by the possible zero using synthetic division. Once you have used synthetic division, your remainder should come out to be zero. However, if your remainder is not zero, the zero we used does not work therefore it is not a rational zero. You then continue testing the zeros until you have found one that has a remainder of zero. Once you have found one that has a remainder of zero, you take that answer you set it up in factored form. The number that is next to your remainder is the constant and the next one has a power of one and so on. After this, you expand this form as far as possible. The amount of zeros you end up with will be the number of parenthetical citations. To find the zeros, you make each parenthesis equal to zero and then solve. Here you use the zero product property. The zero product property states that anything times a zero is zero. In a polynomial function there are also local minimums and maximums. A local maximum is when the graph changes from increasing to decreasing. A local minimum is when the graph changes from decreasing to increasing. The slope at the local minimums and maximums is zero.