Question

Which of the following are polynomials and which are not polynomials?

x^2/7+1
-2x^3+2x+4
x^-3+4x
6x-x^3+4x^2

Answer 1

only (2) and (4) are polynomial out of given options.

Explanation:

Polynomial is an expression having variables having positive integer exponents with real constant coefficients. example
`2x^2+3x+4`

We are given some polynomials and we have to choose whether are polynomial or not.

Consider ,

1)
`x^{(2)/(7)}+1`

Since, Polynomial does not have a fractional exponent.

So, 1) Not a polynomial.

2)
`-2x^3+2x+4`

Since all of the variables have integer exponents that are positive this is a polynomial.

3)
`x^(-3)+4x`

Not a polynomial because a term has a negative exponent .

4)
`6x-x^3+4x^2`

Since all of the variables have integer exponents that are positive this is a polynomial.

Thus, only (2) and (4) are polynomial out of given options.