How Do You Solve a Complex Polynomial and Trigonometry Problem?

[songoku]

Homework Statement

If x³ + 5x² + 4x = 3 = 0 and cos (5 - 3x) = √p, find the value of cot (x⁵ + 2x⁴ - 6x³ + 16x² + 8x + 20)

Homework Equations

trigonometry
polynomial

The Attempt at a Solution

stuck from the beginning...

 

[rock.freak667]

Try modifying x⁵ + 2x⁴ - 6x³ + 16x² + 8x + 20 such that you can pull out (by adding or subtracting) x³ + 5x² + 4x + 3 (which you know to be equal to zero).

 

[songoku]

Try modifying x⁵ + 2x⁴ - 6x³ + 16x² + 8x + 20 such that you can pull out (by adding or subtracting) x³ + 5x² + 4x + 3 (which you know to be equal to zero).

OK. thanks for the help