Polynomial basics
Identify polynomial parts and add or subtract polynomials.
Objective
Identify polynomial parts and add or subtract polynomials.
What it means
A polynomial is a sum of terms with whole-number exponents on the variable. Its degree is the highest exponent present, and its leading coefficient is the number in front of that highest-degree term.
Key terms
- Term
- A single number, variable, or product of numbers and variables
- Degree
- The highest exponent on the variable in the polynomial
- Leading coefficient
- The coefficient of the highest-degree term
- Like terms
- Terms with the same variable raised to the same power
Rules to remember
- Only combine like terms when adding or subtracting.
- The degree of a sum is the highest degree among all terms after combining.
- Distribute a negative sign to every term when subtracting a polynomial.
Step by step
- 1Line up like termsGroup terms with matching variable powers.
- 2Combine coefficientsAdd or subtract the coefficients of like terms only.
- 3Report degree and leading coefficientLook at the surviving highest-power term.
Common mistakes
- Forgetting to distribute the negative sign across all terms when subtracting.
- Combining terms with different exponents.
Tips
- Rewrite polynomials in descending order of exponent before combining.
- The constant term has degree 0.