Lesson OVERVIEW of lessons on solving polynomial equations of high degree

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OVERVIEW of lessons on solving polynomial equations of high degree


This file is an OVERVIEW of my lessons on solving polynomial equations of high degree (Algebra-I curriculum).
For your convenience,  it contains the list of the lessons and then the same list with short annotations to each lesson.

    - Solving polynomial equations of high degree by factoring
    - Solving polynomial equations of high degree by introducing a new variable
    - Advanced factoring
    - Upper_level_miracle_factoring
    - Solving palindromic equations of the degree 4

List of lessons with short annotations


Solving polynomial equations of high degree by factoring

     Problem 1.  Solve an equation   x%5E3%2B2x%5E2-x-2 = 0.

     Problem 2.  Solve an equation   x%5E3+%2B+9x%5E2+%2B+5x = -45.

     Problem 3.  Solve an equation by factoring   x%5E4+%2B+4x%5E3+-+25x%5E2+-+100x = 0.

     Problem 3.  Find the complete factorization of   p(x)= x^4 - 2x^3 + 10x^2 - 18x + 9.


Solving polynomial equations of high degree by introducing a new variable

     Problem 1.  Solve an equation of degree 4   x%5E4 - 13x%5E2 + 36 = 0.

     Problem 2.  Solve an equation of degree 6   x%5E6 + 3x%5E3 + 2 = 0.

     Problem 3.  f(x) = x^3 - 2   and   g(x) = x^2 - 5x.  Solve equation   (gof)(x) = 6.


Advanced factoring

     Problem 1.  Factor   a%5E4+%2B+1.

     Problem 2.  Factor   a%5E4+%2B+4.

     Problem 3.  Prove that   n%5E4+%2B+4   is a composed number for any natural  n.

     Problem 4.  Factor   x%5E4+%2B+x%5E2+%2B+1.

     Problem 5.  Factor   x%5E8+%2B+x%5E4+%2B+1.

     Problem 6.  Factor   x%5E5+%2B+x%5E3+%2B+x.

     Problem 7.  Factor   x%5E4+-+3x%5E2+%2B+1.

     Problem 8.  Given the expression   x2 - kx + 81.
                       a)   Determine the value of  "k"  that makes the trinomial factorable.
                       b)   Factor it for each such value of  "k".


Upper_level_miracle_factoring

     Problem 1.  Factorize   x%5E4+%2B+4%5E2023.


Solving palindromic equations of the degree 4

     Problem 1.  Solve an equation   6x%5E4+-+35x%5E3+%2B+62x%5E2+-+35x+%2B+6 = 0.


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