Solving Polynomials

Introduction to Solving Polynomials:

In math, variables and constants with the operations of addition, subtraction, multiplication, and non-negative, whole-number exponents of finite length is known as a polynomial or in-determinates. For example, x² − 4x + 7 is a polynomial, but x² − 4/x + 7x^3/2 is not, because its second term involves division by the variable x and because its third term contains an exponent that is not a whole number.

Steps to Solve Polynomials:

Generally a polynomial P[x] corresponds to a polynomial function, ƒ(x) = P[x], where the polynomial is set to zero. P[x] =0. The solutions of the equation are called the roots of the polynomial and they are the zeroes of the function. If x = a, is a root of a polynomial, then (x − a) is a factor of that polynomial. The steps to be followed to solve polynomials are as follows

1. If solving an equation, put it in standard form with 0 on one side and simplify.
2. Then know how many roots to expect.
3. If you get a linear or quadratic equation solve it by inspection or the formula. Then go to step 7.
4. Find the rational factor or root. There are lots of techniques to help you. If you can find the factor or root, continue with step 5 below; if you cannot, go to step 6.
5. Divide by your factor, which leaves you with a new reduced polynomial whose degree is ‘1’ less. Then you will work with the reduced polynomial and not with the original one. Continue with step 3.
6. If you cannot find the factors or roots, turn to the numerical methods.
   Then go to step 7.
7. If this was an equation to solve, write down the roots. If it is a polynomial to be factored, write it in the factored form, including any constant factors you took out in step 1.

These are the set of steps that will lead to a desired result in a finite number of operations. It is an iterative strategy.