Question

which is true about the polynomial $-3xy^2 + 5x^2y$?

• it is a binomial with a degree of 2.
• it is a binomial with a degree of 3.
• it is a trinomial with a degree of 2.
• it is a trinomial with a degree of 3.

Explanation:

Step1: Identify the number of terms

The polynomial is \(-3xy^{2}+5x^{2}y\). A term is a single mathematical expression, so here we have two terms: \(-3xy^{2}\) and \(5x^{2}y\). So it's a binomial (since binomial has 2 terms, trinomial has 3).

Step2: Find the degree of each term

For a term with variables, the degree is the sum of the exponents of the variables.

• For \(-3xy^{2}\): exponent of \(x\) is \(1\), exponent of \(y\) is \(2\). So degree is \(1 + 2=3\).
• For \(5x^{2}y\): exponent of \(x\) is \(2\), exponent of \(y\) is \(1\). So degree is \(2 + 1 = 3\).

The degree of the polynomial is the highest degree of its terms, so the degree is \(3\).

Answer:

It is a binomial with a degree of 3.