I have been struggling to create a polynomial that adheres to the following guidelines and I am hoping someone can help me out. I have a series of questions regarding the polynomial and I am struggling to get past the first step, creating the polynomial itself.
Create a polynomial in standard form of least degree with integer coefficients that has 5 – 2i, √3, 0, and -1 as zeros. Show your work.
Check that your answer is correct by using division. Show your work, and make it clear and organized.
Show that 1 is not a zero of the polynomial
What is the end behavior of your polynomial?
How many real zeros, irrational zeros, and imaginary zeros does it have, respectively?
What is the degree of your polynomial?
Use your calculator to determine the
a. Relative maxima
b. Relative minima
c. Intervals over which the polynomial is increasing
d. Intervals over which the polynomial is decreasing
Does your polynomial have an absolute maximum? If so, what is it?
Does your polynomial have an absolute minimum? If so, what is it?