Question

what is true about the polynomial -3xy² + 5x²y? be sure to include information about whether its a binomial or trinomial, the degree of the polynomial, and what the coefficients are. 0 / 10000 word limit

Explanation:

Step1: Define degree of polynomial

The degree of a term in a polynomial in two - variables \(x\) and \(y\) is the sum of the exponents of \(x\) and \(y\) in that term. For the term \(- 3xy\), the sum of exponents of \(x\) and \(y\) is \(1 + 1=2\). For the term \(5x^{2}y\), the sum of exponents of \(x\) and \(y\) is \(2 + 1 = 3\). The degree of a polynomial is the highest degree of its terms. So the degree of the polynomial \(-3xy + 5x^{2}y\) is 3.

Step2: Identify coefficients

The coefficient of a term is the numerical factor. For the term \(-3xy\), the coefficient is \(-3\). For the term \(5x^{2}y\), the coefficient is 5.

Step3: Determine type

A binomial has two terms, and the given polynomial \(-3xy+5x^{2}y\) has two terms, so it is a binomial.

Answer:

Degree: 3; Coefficients: - 3 and 5; It is a binomial.