Polynomial Degree and Leading Coefficient

1) What to identify

For each polynomial, focus on the term with the highest power of the variable. That power is the degree of the polynomial. The coefficient attached to that term is the leading coefficient.

2) How to find them

1. Write the polynomial in standard form if it is not already: terms should be arranged from highest exponent to lowest exponent.
2. Find the highest exponent. That exponent is the degree.
3. Look at the coefficient of that term. That number is the leading coefficient.
4. If the highest-power term is written with a negative sign, the leading coefficient is negative.

3) Important checks

• If a polynomial has only a constant term, its degree is 0.
• If the variable disappears after simplification, simplify first and then re-check the highest remaining power.
• Make sure you do not confuse the degree with the number of terms.

4) Final check

After identifying the degree and leading coefficient, reread the simplified polynomial and confirm that no term has a higher exponent than the one you chose. Your final answer should clearly state both values.