Question

what is the degree of the polynomial $2x - x^2 + 4x^3$?
(1) 1
(2) 2
(3) 3
(4) 4

Explanation:

Step1: Recall the definition of the degree of a polynomial

The degree of a polynomial is the highest power (exponent) of the variable in the polynomial.

Step2: Identify the exponents of each term in the polynomial \(2x - x^{2}+4x^{3}\)

• For the term \(2x\), the exponent of \(x\) is \(1\).
• For the term \(-x^{2}\), the exponent of \(x\) is \(2\).
• For the term \(4x^{3}\), the exponent of \(x\) is \(3\).

Step3: Determine the highest exponent

Among the exponents \(1\), \(2\), and \(3\), the highest one is \(3\).

Answer:

(3) 3