Which polynomial has a degree of 4?

Which polynomial has a degree of 4?

• A. 3x^2 + x + 1
• B. 5x^4 - 3x^3 + 2
• C. 2x^5 - x^2 + 4
• D. x - 6

Answer: (B)

To determine the degree of a polynomial, you need to identify the highest power of the variable (in this case, \(x\)) that appears in the polynomial. The degree of a polynomial is defined by the term with the largest exponent. In the given options, we can analyze the polynomials as follows: - The first polynomial, \(3x^2 + x + 1\), has a highest exponent of 2, indicating that it is a degree 2 polynomial. - The second polynomial, \(5x^4 - 3x^3 + 2\), features the term \(5x^4\), where the highest exponent is 4. Therefore, this is a degree 4 polynomial. - The third polynomial, \(2x^5 - x^2 + 4\), has a highest exponent of 5, making it a degree 5 polynomial. - The fourth polynomial, \(x - 6\), contains the variable \(x\) raised to the first power, resulting in a degree of 1. Given this analysis, the polynomial \(5x^4 - 3x^3 + 2\) clearly stands out with the highest degree of 4, confirming that it

To determine the degree of a polynomial, you need to identify the highest power of the variable (in this case, (x)) that appears in the polynomial. The degree of a polynomial is defined by the term with the largest exponent.

In the given options, we can analyze the polynomials as follows:

• The first polynomial, (3x^2 + x + 1), has a highest exponent of 2, indicating that it is a degree 2 polynomial.

• The second polynomial, (5x^4 - 3x^3 + 2), features the term (5x^4), where the highest exponent is 4. Therefore, this is a degree 4 polynomial.

• The third polynomial, (2x^5 - x^2 + 4), has a highest exponent of 5, making it a degree 5 polynomial.

• The fourth polynomial, (x - 6), contains the variable (x) raised to the first power, resulting in a degree of 1.

Given this analysis, the polynomial (5x^4 - 3x^3 + 2) clearly stands out with the highest degree of 4, confirming that it