To determine the degree of the polynomial [tex]\(12x^4 - 8x + 4x^2 - 3\)[/tex], we need to identify the highest power of the variable [tex]\(x\)[/tex] in the polynomial.
Here are the steps to find the degree of the polynomial:
1. Identify Each Term and Its Degree:
- The polynomial is given by [tex]\(12x^4 - 8x + 4x^2 - 3\)[/tex].
- The first term is [tex]\(12x^4\)[/tex], with a degree of 4.
- The second term is [tex]\(-8x\)[/tex], with a degree of 1.
- The third term is [tex]\(4x^2\)[/tex], with a degree of 2.
- The fourth term is [tex]\(-3\)[/tex], which is a constant term and has a degree of 0.
2. Find the Highest Degree:
- Among the degrees of the terms (4, 1, 2, and 0), the highest degree is 4.
3. Conclusion:
- The degree of the polynomial is the highest degree among all the terms, which is 4.
Therefore, the degree of the polynomial [tex]\(12x^4 - 8x + 4x^2 - 3\)[/tex] is [tex]\(4\)[/tex].
The correct answer is:
C. 4
