Question

Which expressions are polynomials?

Select each correct answer.



Responses

20x²
20 x ²

20x² + y
20 x ² + y

20x2y
fraction numerator 20 x squared end numerator over y end fraction

20x2+y12

Answer 1

To determine which expressions are polynomials, we need to remember that a polynomial is an expression made up of variables raised to non-negative integer powers, with coefficients that can be any real number.

Let's evaluate each of the provided expressions:

1. **20x²** - This is a polynomial because it is a single term with a variable raised to a non-negative integer power.

2. **20 x ²** - This is essentially the same as the first expression, just written with a space. It is also a polynomial.

3. **20x² + y** - This is a polynomial because it consists of terms (20x² and y) where both terms are either constants or variables raised to non-negative integer powers.

4. **20x2y** - Here, "x2" seems to refer to "x squared". If this means \(20x^2y\), then this is a polynomial because it consists of terms where each variable is raised to a non-negative integer power. Note: if "x2" is read as "x" and "2" are separate symbols, then it's not a polynomial.

5. **fraction numerator 20 x squared end numerator over y end fraction** - This is a fraction, and because it contains division by \(y\), it is NOT a polynomial. Polynomials cannot have variables in the denominator.

6. **20x2 + y12** - Assuming "y12" refers to \(y^{12}\) (y raised to the 12th power), then this expression, \(20x^2 + y^{12}\), is a polynomial since both terms have non-negative integer powers.

Based on this analysis, the expressions that are polynomials are:

- 20x²
- 20 x ²
- 20x² + y
- 20x2 + y12 (assuming y12 is interpreted as \(y^{12}\))

So, the correct responses are:

1. **20x²**
2. **20 x ²**
3. **20x² + y**
4. **20x2 + y12** (if interpreted as \(20x^2 + y^{12}\))