Question

what is the degree of the polynomial function p(x)=3x⁴ - 7x² - 2x⁷ - x + 4? options: 7, 2, 1, 4

Explanation:

Step1: Recall the definition of the degree of a polynomial

The degree of a polynomial is the highest power (exponent) of the variable in the polynomial.

Step2: Identify the exponents of each term in \( P(x) = 3x^{4}-7x^{2}-2x^{7}-x + 4\)

• For the term \(3x^{4}\), the exponent is \(4\).
• For the term \(-7x^{2}\), the exponent is \(2\).
• For the term \(-2x^{7}\), the exponent is \(7\).
• For the term \(-x\) (which can be written as \(-x^{1}\)), the exponent is \(1\).
• For the constant term \(4\) (which can be written as \(4x^{0}\)), the exponent is \(0\).

Step3: Determine the highest exponent

Among the exponents \(4\), \(2\), \(7\), \(1\), and \(0\), the highest one is \(7\).

Answer:

7 (corresponding to the green option with "7")