What is the degree of $x^5-4 x+2$?
A. 6
B. 4
C. 3
D. 5
Answer (1)
The degree of a polynomial is the highest power of the variable.
Identify the term with the highest power of x in the polynomial x 5 − 4 x + 2 .
The term with the highest power is x 5 , so the degree of the polynomial is 5.
The degree of the polynomial is 5 .
Explanation
Identifying the Degree The degree of a polynomial is the highest power of the variable in the polynomial. In the polynomial x 5 − 4 x + 2 , we need to identify the term with the highest power of x .
Determining the Highest Power The terms in the polynomial are x 5 , − 4 x , and 2 . The powers of x in these terms are 5, 1, and 0, respectively (since 2 = 2 x 0 ).
Concluding the Degree The highest power of x in the polynomial x 5 − 4 x + 2 is 5. Therefore, the degree of the polynomial is 5.
Examples
Understanding the degree of a polynomial is crucial in many areas of mathematics and physics. For instance, when analyzing the motion of an object, the equation describing its position as a function of time might be a polynomial. The degree of this polynomial can tell us about the complexity of the motion. A linear polynomial (degree 1) represents constant velocity, while a quadratic polynomial (degree 2) represents constant acceleration. Higher degree polynomials can model more complex motions, such as oscillations or damped oscillations. Knowing the degree helps in predicting the object's behavior and understanding the underlying physics.
