Question

question 1
1 pts
which expressions are polynomials?
select each correct answer.
□ \\(\frac{30y^2}{x}\\)
□ \\(30y^2 + x^{\frac{1}{2}}\\)
□ \\(30y^2 + x\\)
□ \\(30y^2\\)

Explanation:

Step1: Recall Polynomial Definition

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non - negative integer exponents of variables.

Step2: Analyze \(\frac{30y^{2}}{x}\)

We can rewrite \(\frac{30y^{2}}{x}\) as \(30y^{2}x^{- 1}\). Here, the exponent of \(x\) is \(- 1\), which is a negative integer. So, this expression is not a polynomial.

Step3: Analyze \(30y^{2}+x^{\frac{1}{2}}\)

The exponent of \(x\) in the term \(x^{\frac{1}{2}}\) is \(\frac{1}{2}\), which is not a non - negative integer. So, this expression is not a polynomial.

Step4: Analyze \(30y^{2}+x\)

In the term \(30y^{2}\), the exponent of \(y\) is \(2\) (a non - negative integer), and in the term \(x\), the exponent of \(x\) is \(1\) (a non - negative integer). The operations involved are addition, multiplication (implicit in the coefficient - variable multiplication), and the exponents are non - negative integers. So, this is a polynomial.

Step5: Analyze \(30y^{2}\)

The term \(30y^{2}\) has a variable \(y\) with an exponent of \(2\) (a non - negative integer) and a coefficient \(30\). The operation is multiplication (implicit), and the exponent is a non - negative integer. So, this is a polynomial.

Answer:

\(30y^{2}+x\), \(30y^{2}\)