Question

What is the correct name of the following
3x + 5y^2 - 3

Answer 1

The options are

monomial
monomial

binomial
binomial

trinomial
trinomial

not a polynomial

Answer 2

The expression \(3x + 5y^2 - 3\) is a polynomial. Specifically, it is a polynomial in two variables, \(x\) and \(y\).

To be more specific:
- The term \(3x\) is a linear term in \(x\).
- The term \(5y^2\) is a quadratic term in \(y\).
- The term \(-3\) is a constant.

The degree of the polynomial is determined by the highest degree of its terms. Here, the degree of \(5y^2\) is 2 (since the exponent of \(y\) is 2) and the degree of \(3x\) is 1, making the overall degree of the polynomial 2.

So, the expression \(3x + 5y^2 - 3\) can be correctly described as a **degree 2 polynomial in two variables**.

Answer 3

The expression \(3x + 5y^2 - 3\) is a **trinomial** because it contains three terms: \(3x\), \(5y^2\), and \(-3\).

So, the correct option is **trinomial**.