Lesson OVERVIEW of lessons on solving polynomial equations of high degree

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<H2>OVERVIEW of lessons on solving polynomial equations of high degree</H2>

This file is an OVERVIEW of my lessons on solving polynomial equations of high degree (Algebra-I curriculum).

For your convenience, &nbsp;it contains the list of the lessons and then the same list with short annotations to each lesson.

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/81-Solving-polynomial-equations-of-high-degree-by-factoring.lesson>Solving polynomial equations of high degree by factoring</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Solving-polynomial-equations-of-high-degree-by-introducing-a-new-variable.lesson>Solving polynomial equations of high degree by introducing a new variable</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Advanced-factoring.lesson>Advanced factoring</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Upper-level-miracle-factoring.lesson>Upper_level_miracle_factoring</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Solving-palindromic-equations-of--the-degree-4.lesson>Solving palindromic equations of the degree 4</A>

<H3>List of lessons with short annotations</H3>

<A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/81-Solving-polynomial-equations-of-high-degree-by-factoring.lesson>Solving polynomial equations of high degree by factoring</A>

&nbsp;&nbsp;&nbsp;&nbsp; Problem 1. &nbsp;Solve an equation &nbsp;&nbsp;{{{x^3+2x^2-x-2}}} = {{{0}}}.

&nbsp;&nbsp;&nbsp;&nbsp; Problem 2. &nbsp;Solve an equation &nbsp;&nbsp;{{{x^3 + 9x^2 + 5x}}} = {{{-45}}}.

&nbsp;&nbsp;&nbsp;&nbsp; Problem 3. &nbsp;Solve an equation by factoring &nbsp;&nbsp;{{{x^4 + 4x^3 - 25x^2 - 100x}}} = {{{0}}}.

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

<A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Solving-polynomial-equations-of-high-degree-by-introducing-a-new-variable.lesson>Solving polynomial equations of high degree by introducing a new variable</A>

&nbsp;&nbsp;&nbsp;&nbsp; Problem 1. &nbsp;Solve an equation of degree 4 &nbsp;&nbsp;{{{x^4}}} - {{{13x^2}}} + {{{36}}} = {{{0}}}.

&nbsp;&nbsp;&nbsp;&nbsp; Problem 2. &nbsp;Solve an equation of degree 6 &nbsp;&nbsp;{{{x^6}}} + {{{3x^3}}} + {{{2}}} = {{{0}}}.

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

<A HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Advanced-factoring.lesson>Advanced factoring</A>

&nbsp;&nbsp;&nbsp;&nbsp; Problem 1. &nbsp;Factor &nbsp;&nbsp;{{{a^4 + 1}}}.

&nbsp;&nbsp;&nbsp;&nbsp; Problem 2. &nbsp;Factor &nbsp;&nbsp;{{{a^4 + 4}}}.

&nbsp;&nbsp;&nbsp;&nbsp; Problem 3. &nbsp;Prove that &nbsp;&nbsp;{{{n^4 + 4}}}&nbsp;&nbsp; is a composed number for any natural &nbsp;n.

&nbsp;&nbsp;&nbsp;&nbsp; Problem 4. &nbsp;Factor &nbsp;&nbsp;{{{x^4 + x^2 + 1}}}.

&nbsp;&nbsp;&nbsp;&nbsp; Problem 5. &nbsp;Factor &nbsp;&nbsp;{{{x^8 + x^4 + 1}}}.

&nbsp;&nbsp;&nbsp;&nbsp; Problem 6. &nbsp;Factor &nbsp;&nbsp;{{{x^5 + x^3 + x}}}.

&nbsp;&nbsp;&nbsp;&nbsp; Problem 7. &nbsp;Factor &nbsp;&nbsp;{{{x^4 - 3x^2 + 1}}}.

&nbsp;&nbsp;&nbsp;&nbsp; Problem 8. &nbsp;Given the expression &nbsp;&nbsp;x2 - kx + 81.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;a) &nbsp;&nbsp;Determine the value of &nbsp;"k" &nbsp;that makes the trinomial factorable.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;b) &nbsp;&nbsp;Factor it for each such value of  &nbsp;"k".

<A HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Upper-level-miracle-factoring.lesson>Upper_level_miracle_factoring</A>

&nbsp;&nbsp;&nbsp;&nbsp; Problem 1. &nbsp;Factorize &nbsp;&nbsp;{{{x^4 + 4^2023}}}.

<A HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Solving-palindromic-equations-of--the-degree-4.lesson>Solving palindromic equations of the degree 4</A>

&nbsp;&nbsp;&nbsp;&nbsp; Problem 1. &nbsp;Solve an equation &nbsp;&nbsp;{{{6x^4 - 35x^3 + 62x^2 - 35x + 6}}} = {{{0}}}.

Use this file/link &nbsp;<A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>&nbsp; to navigate over all topics and lessons of the online textbook &nbsp;ALGEBRA-I.