What is the degree of $12 x^4-8 x+4 x^2-3$?
A. 4
B. 3
C. 12
D. 8
Answer (1)
Identify the highest power of the variable x in the polynomial.
The highest power of x in 12 x 4 − 8 x + 4 x 2 − 3 is 4.
Therefore, the degree of the polynomial is 4.
The final answer is 4 .
Explanation
Understanding the Problem We are asked to find the degree of the polynomial 12 x 4 − 8 x + 4 x 2 − 3 . The degree of a polynomial is the highest power of the variable in the polynomial.
Identifying the Powers of x The given polynomial is 12 x 4 − 8 x + 4 x 2 − 3 . The terms of the polynomial are 12 x 4 , − 8 x , 4 x 2 , and − 3 . The powers of x in these terms are 4, 1, 2, and 0, respectively.
Determining the Degree The highest power of x in the polynomial is 4. Therefore, the degree of the polynomial is 4.
Examples
Understanding the degree of a polynomial is crucial in many areas, such as physics, engineering, and computer science. For example, in physics, the trajectory of a projectile can be modeled by a quadratic equation (a polynomial of degree 2). In engineering, polynomial functions are used to model various systems and processes. In computer science, polynomials are used in cryptography and data compression. Knowing the degree of a polynomial helps us understand the complexity and behavior of these models and systems.
