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There are 5 lessons in this math tutorial covering Solutions for Polynomial Equations. The tutorial starts with an introduction to Solutions for Polynomial Equations and is then followed with a list of the separate lessons, the tutorial is designed to be read in order but you can skip to a specific lesson or return to recover a specific math lesson as required to build your math knowledge of Solutions for Polynomial Equations. you can access all the lessons from this tutorial below.
In this Math tutorial, you will learn:
So far, we have reviewed several situations where the problem asked us to calculate the zeroes of a polynomial. We completed these in a number of ways. In first-degree polynomials, this was an easy task as these polynomials have a single zero (the root of the corresponding linear equation with one variable). In second-degree polynomial, we used either factorisation or the quadratic formula to find the two possible zeroes. In third-degree polynomials, we mostly suggested the iterative methods to find the roots, as they rarely correspond to whole numbers. In other cases, we divided the given polynomial by another supposedly polynomial factor by applying the polynomial division rules.
Obviously, all of these methods have their limitations and are used only in specific contexts. It is important therefore to find a method that is more comprehensive and usable. This method is called "the Synthetic Division Method of Polynomials" - a method that we are going to present in this tutorial. This method is combined with an important algebra theorem known as the "Rational Root (or Rational Zero) Theorem", which is used to prove the correctness of the division method mentioned above. When combined, the above methods help to identify the zeroes of any polynomial with integer coefficients and to find all possible factorisation of the original polynomial.
Identifying the zeroes of a polynomial P(x) means finding the solution of the polynomial equation P(x) = 0, which is the main objective of this tutorial.
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