Princeton University Polynomial and Rational Function Math Questions

Explain each step and show your work.

state and show all formulas used…………..needed in four hours

Answer any three of the following
Show your working and explain each step
Q1
Describe a polynomial and a rational function. Include any relevant terms and their application
as needed.
Explain how to divide polynomials. Give examples to support your response.
Q2
How do you solve this integral of 3 sec(2x-1)tan(2x-1)?
Q4
The function f(z) is complex valued in the complex plane. f(z) is bounded and entire.
Prove that f(z) must be a constant.
Q5
Divide. (6x^2+27x+8)/(x+4). Your answer should give the quotient and the remainder.
Please discuss the steps you took to arrive at your answer.
Q6
Can trigonometry be used to prove the Pythagorean theorem? Please provide an
explanation and examples for your answer following MLA Guidelines.
Q7
please solve: Solve log ( 2x + 1 ) – log 6 = 2 for x. Please explain how you arrived at
your answer. Thanks!
Q8
How many consecutive zeroes are there at the end of 100! (100 factorial). For example,
12! – 479,001,600 has two consecutive zeroes at the end.