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How to Determine If a Sum of Terms Is a Polynomial?

All polynomials are a sum of terms, though not all sums of terms are polynomials. A term is simply any individual entity, such as a number like "9" or a variable such as "x," and the sum of terms is the result when you add together terms. A polynomial is a sum of terms that still has an addition symbol in it because some of the terms cannot be simplified further (such as "3x + 9" or "2a + 3b + 4c").

Instructions

- 1
  Simplify the equation. If all the like terms (terms that share the same variable or multiple constants) have not been simplified, you cannot know if the sum of terms is a polynomial.
- 2
  Observe if there is still more than one term after simplifying. If there is, the sum of terms is a polynomial. Make sure an addition symbol is present.
- 3
  Determine the polynomial by its degree. A polynomial's degree is the highest power to which a variable is raised; thus, "9x^3 + 1" is a third-degree polynomial (called a "cubic").

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