Question: The image contains a mathematical expression and a set of options. The expression is: \[…

The image contains a mathematical expression and a set of options. The expression is:

\[ 4\sqrt{x} + y^2 \]

The options are:

• none of these
• trinomial
• monomial
• polynomial
• binomial

The feedback at the bottom of the image states: “That’s not it.”

Solution

To classify the expression \(4\sqrt{x} + y^2\): The expression is composed of two terms: \(4\sqrt{x}\) and \(y^2\). A polynomial is an algebraic expression consisting of variables and coefficients, formed using only addition, subtraction, multiplication, and non-negative integer exponents of variables. In this expression: - \(4\sqrt{x}\) involves a square root, which is equivalent to \(x^{1/2}\) and does not have a non-negative integer exponent, so it is not a polynomial term. - \(y^2\) is a polynomial term. Since the expression contains a term that is not a polynomial term, the entire expression \(4\sqrt{x} + y^2\) is not a polynomial. Therefore, the correct classification is: - None of these The selected answers “polynomial” and “binomial” are incorrect.