Evaluate a Polynomial

Evaluating a Polynomial

To evaluate a polynomial, replace the variable with the given value and simplify carefully. The goal is to find the polynomial’s numerical value at that input.

Step-by-step method

1. Substitute the value for the variable everywhere it appears.
2. Use parentheses when you replace the variable, especially if the value is negative.
3. Apply order of operations:
   • Do exponents first.
   • Then multiplication and division.
   • Then addition and subtraction.
4. Combine all terms to get a single simplified number.

Important caution

If the input is negative, parentheses help prevent sign mistakes. For example, if a term contains (x^2) and (x=-3), then ((-3)^2=9), not (-9).

Check your work

Recalculate each term separately before combining them. Make sure the signs are correct and that every occurrence of the variable was replaced.

Example structure

For a polynomial like (2x^2-3x+1), first substitute the given value for (x), then compute each part in order, and finally combine the results.

A correct final answer should be fully simplified and written as a number, not as an expression with variables.