Question

find the degree of the polynomial and indicate whether the polynomial is a monomial, bin\\(x^{2}y - 8xy^{2} + 6x + y^{7}\\)\
the degree of the polynomial is \\(\square\\).

Explanation:

Step1: Recall the degree of a term

The degree of a term with variables is the sum of the exponents of the variables. For example, for a term \(ax^{m}y^{n}\), the degree is \(m + n\).

Step2: Find the degree of each term

• For the term \(x^{2}y\): The exponent of \(x\) is \(2\) and the exponent of \(y\) is \(1\), so the degree is \(2+ 1=3\).
• For the term \(-8xy^{2}\): The exponent of \(x\) is \(1\) and the exponent of \(y\) is \(2\), so the degree is \(1 + 2=3\).
• For the term \(6x\): The exponent of \(x\) is \(1\) (and \(y\) has exponent \(0\) if we consider \(y\)), so the degree is \(1+0 = 1\).
• For the term \(y^{7}\): The exponent of \(y\) is \(7\) (and \(x\) has exponent \(0\)), so the degree is \(7+0=7\).

Step3: Determine the degree of the polynomial

The degree of a polynomial is the highest degree among its terms. From the degrees of the terms (\(3\), \(3\), \(1\), \(7\)), the highest degree is \(7\).

Answer:

\(7\)