A linear polynomial is a polynomial of the first degree. This means that no variable will have an exponent greater than one. Because this is a first-degree polynomial, it will have exactly one real 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). 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 coefficient. 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}}}.
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