Algebra 1 · Unit 7 · Topic 7.3
Polynomials, Degree, and Addition
A polynomial in x is a sum of terms axⁿ where each exponent n is a nonnegative integer.
Definition and explanation
A polynomial in x is a sum of terms axⁿ where each exponent n is a nonnegative integer. Its degree is the largest exponent with a nonzero coefficient; addition and subtraction combine like terms.
Worked example
Add (3x² − 4x + 1) and (−x² + 6x − 5). Combining matching powers gives 2x² + 2x − 4, a degree-2 polynomial.
Common mistake
Expressions with x in a denominator or with √x are not polynomials in x.
Key takeaway
A polynomial in x is a sum of terms axⁿ where each exponent n is a nonnegative integer.
Explain each step of the worked example, then check the units, signs, and conditions that apply.
Further reading
Topic coverage was checked against the openly available OpenStax Elementary Algebra 2e and Algebra and Trigonometry 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.