The degree of the polynomial function below is
[tex]$f(x)=-3 x^5+4 x-2$[/tex]
Answer (1)
Identify the term with the highest power of x: − 3 x 5 .
Determine the exponent of that term: 5 .
The degree of the polynomial is the exponent of the term with the highest power.
The degree of the polynomial f ( x ) = − 3 x 5 + 4 x − 2 is 5 .
Explanation
Identifying the highest power We are given the polynomial function f ( x ) = − 3 x 5 + 4 x − 2 . The degree of a polynomial is the highest power of the variable x in the polynomial. In this case, we need to identify the term with the highest power of x .
Determining the exponents The terms in the polynomial are − 3 x 5 , 4 x , and − 2 . The powers of x in these terms are 5 , 1 , and 0 (since − 2 = − 2 x 0 ), respectively.
Concluding the degree The highest power of x is 5 . Therefore, the degree of the polynomial f ( x ) = − 3 x 5 + 4 x − 2 is 5 .
Examples
Understanding the degree of a polynomial is crucial in many areas, such as physics and engineering. For instance, when modeling the trajectory of a projectile, the equation might be a quadratic polynomial (degree 2). Knowing the degree helps predict the behavior of the projectile, like its maximum height and range. Similarly, in circuit analysis, polynomial functions can describe the behavior of current and voltage, and the degree of the polynomial can indicate the complexity of the circuit's response.
