Question

For the polynomial 3x²y−5y²−xy²x−7, what is the degree of the polynomial?

a) 1
b) 2
c) 3
d) 4

Answer 1

The degree of the polynomial 3x^2y - 5y^2 - xy^2 + x - 7 is 3, which is the highest sum of exponents on the variables in any single term of the polynomial.

Step-by-step explanation:

The degree of a polynomial is the highest degree of any of its individual terms. For the polynomial \(3x^2y - 5y^2 - xy^2 + x - 7\), we need to find the term with the highest sum of exponents on the variables. Let's consider each term:

• \(3x^2y\): Degree is \(2 + 1 = 3\)
• \(-5y^2\): Degree is \(2\)
• \(-xy^2\): Degree is \(1 + 2 = 3\)
• \(x\): Degree is \(1\)
• \(-7\): Degree is \(0\) because this is a constant term.

Therefore, the highest degree among the terms is \(3\), which makes the degree of the whole polynomial \(3\).