This problem goes over finding real and complex zeroes if you are given a 4th or 5th degree polynomial. In this case, we are given a 4th degree polynomial. The first thing that needs to be done in order to find the zeroes of the polynomial is to use the rational roots theorem. You find the factors of p and q and use the equation p/q to find the possible rational zeroes. Next you use Descartes rule of signs to find the possible number or real zeroes (positive or negative). Then you put the possible rational zeroes to work by using them as the divisors in synthetic division as you divide the polynomial. You use synthetic division to decrease the power of the polynomial to a quadratic. From there, you use the quadratic formula to find the remaining zeroes.
There are some things that you need to pay special attention to. The first thing that you have to pay attention to is that you place the p's over the q's, not the q's over the p's! Also, when using Descartes rule of signs, it's important that you flip the odd powered exponents in order to find the correct number of possible real zeroes. Also, throughout the process of the equation, you have to be careful that you are multiplying, dividing, adding, and subtracting correctly, as those little mistakes can make a huge difference in the final answer.
^FINAL ZEROES^
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