Descartes rule of signs

Question

Assignment:

Q1. Use the Rational Zero Theorem to list possible rational zeros for the polynomial:

P(x) = x³ + 3x² - 6x - 8 

Q2. Use Descartes’ Rule of Signs to determine both the number of possible positive and the number of possible negative real zeros of the polynomial.

P(x) = 2x³ + x² - 25x + 12
 
Q3. Use the given zero to find the remaining zeros of the polynomial.
P(x) = 3x³ - 29x² + 92x + 34
 
The given zero = 5 + 3i

Q4. Determine the vertical and horizontal asymptotes and sketch the graph of the rational function F(x). Label all intercepts and asymptotes.

f(x) =  - 4 / (x - 3)

Q5. Write the logarithmic expression as a single logarithm.

log₁₀(x + 5) + 2log₁₀x

Provide complete and step by step solution for the question and show calculations and use formulas.