What is the degree of the polynomial 5x^4 + 2x^2 - x + 9?

• A. 4
• B. 2
• C. 3
• D. 1

Answer: (A)

The degree of a polynomial is the largest power of x that appears with a nonzero coefficient. In 5x^4 + 2x^2 - x + 9, the exponents present are 4, 2, 1, and 0. The highest is 4, so the degree is 4. The leading term 5x^4 dominates the polynomial’s growth, and the other terms do not change this degree. If the x^4 term were absent, the degree would drop to 2 due to the 2x^2 term.