How Do You Solve a Complex Polynomial and Trigonometry Problem?

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SUMMARY

The discussion focuses on solving the complex polynomial equation x3 + 5x2 + 4x - 3 = 0 alongside the trigonometric equation cos(5 - 3x) = √p. A key strategy suggested involves modifying the polynomial expression x5 + 2x4 - 6x3 + 16x2 + 8x + 20 to factor out the known polynomial x3 + 5x2 + 4x + 3, which equals zero. This approach aims to simplify the problem and facilitate finding the value of cot(x5 + 2x4 - 6x3 + 16x2 + 8x + 20).

PREREQUISITES
  • Understanding of polynomial equations, specifically cubic polynomials.
  • Knowledge of trigonometric functions and their properties.
  • Familiarity with factoring techniques in algebra.
  • Ability to manipulate and simplify complex expressions.
NEXT STEPS
  • Study polynomial long division to simplify complex polynomial expressions.
  • Learn about trigonometric identities and their applications in solving equations.
  • Explore methods for solving cubic equations, including the Rational Root Theorem.
  • Investigate cotangent and its relationship with other trigonometric functions.
USEFUL FOR

Students tackling advanced algebra and trigonometry problems, educators seeking teaching strategies for polynomial and trigonometric concepts, and anyone interested in mathematical problem-solving techniques.

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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...:-p
 
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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).
 
rock.freak667 said:
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
 

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