Question

Which expressions are polynomials?

Select each correct answer.





30y2+x


30y2+x12


30y2x


30y2

Answer 1

Option 1 and 2 are polynomials.

Explanation:

To find : Which expressions are polynomials?

Solution :

Polynomials is defined as algebraic expressions which is form by combining numbers and variables using arithmetic operations such as addition, subtraction, multiplication, division, and exponentiation.

Now we examine the given expression,

1)
`30y^2+x`

The expression has got more than one term.

So, it is a polynomial.

2)
`30y^2+x^(12)`

The expression has got more than one term.

So, it is a polynomial.

3)
`30y^2x`

The expression has got just one term.

So, it is not a polynomial.

4)
`30y^2`

The expression has got just one term.

So, it is not a polynomial.

Therefore, Option 1 and 2 are polynomials.

Answer 2

Answer: 30y2+x and 30y2+x12

Explanation:

A polynomial is an algebraic expression consisting of more than one term.

In thise sense, the algebraic expressions are composed of several elements: Terms, Coefficients, Signs, Variables and Exponents. In this case we will focus on the first.

The terms are composed of sign, coefficient, variable and exponent. The terms are separated from each other by the plus sign (+) or the minus sign (-).

For example, in the following expression:

2x-3x

We have two terms separated by the negative sign (-):

2x is the first term

-3x is the second term

Now, according to this explanation, the only two options that have more than one term to be called a polynomial (poly means many and nomial means terms) are the first two:

30y2+x and 30y2+x12