How to Solve Polynomials

Step-by-Step Guide

1. 1

   Step 1: Determine whether you have a linear polynomial.

   A linear polynomial is a polynomial to the first degree.This means that no variable will have an exponent (or an exponent greater than 1).
   
   Because this is a first-degree polynomial, it will have exactly one root, or solution.For example, 5x+2{\displaystyle 5x+2} is a linear polynomial, because the variable x{\displaystyle x} has no exponent (which is the same as an exponent of 1).
2. 2

   Step 2: Set the equation to equal zero.

   This is a necessary step for solving all polynomials.
   
   For example, 5x+2=0{\displaystyle 5x+2=0} , To do this, add or subtract the constant from both sides of the equation.
   
   A constant is a term without a variable.For example, to isolate the x{\displaystyle x} term in 5x+2=0{\displaystyle 5x+2=0}, you would subtract 2{\displaystyle 2} from both sides of the equation:5x+2=0{\displaystyle 5x+2=0}5x+2−2=0−2{\displaystyle 5x+2-2=0-2}5x=−2{\displaystyle 5x=-2} , Usually you will need to divide each side of the equation by the constant.
   
   This will give you the root, or solution, to your polynomial.
   
   For example, to solve for x{\displaystyle x} in 5x=−2{\displaystyle 5x=-2}, you would divide each side of the equation by 5{\displaystyle 5}:5x=−2{\displaystyle 5x=-2}5x5=−25{\displaystyle {\frac {5x}{5}}={\frac {-2}{5}}}x=−25{\displaystyle x={\frac {-2}{5}}}So, the solution to 5x+2{\displaystyle 5x+2} is x=−25{\displaystyle x={\frac {-2}{5}}}.
3. 3

   Step 3: Isolate the variable term.

4. 4

   Step 4: Solve for the variable.

Detailed Guide

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