Graphs of basic functions & Remainder-Factor theorem

Hello! I have a few questions regarding the graphs of basic functions (eg. y = x^3). Please provide explanations to the answers if possible! Thank You very much!

Q1) Construct a cubic equation that describes a graph that has no stationary points. Describe how you arrived at your equation.

Q2) It is not possible to construct a cubic equation that describes a graph that does not intersect with the x-axis. Why not? State and explain using the Remainder and Factor Theorem.

Q3) Given that the 2 quadratic equations:

x^2 -nx -36 = 0

n + 6x - x^2 = 0

have a common root x = a for certain values of the real constant n, show that a^3 - 7(a^2) + 36 = 0

Hence find the possible values of a, and the corresponding values of n. :(

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Thank you very much!