Question

Which expressions are polynomials? Select each correct answer. 30y^2 30y^2+x 30y2x 30y2+x12

Answer 1

To know which of the following expressions are polynomials, let us look at the definition of a polynomial:

Polynomial is derived from poly- (which means "many") and -nomial (meaning "term"), so it says "many terms".

For an instance: $2x^2y+2y^2$ is a polynomial, but $4xy^2$ is not a polynomial because it contains single term only.

We must keep in mind that in polynomial it can have variables, constants, and exponents but it can never have division by a variable.

Now lets, look at the

$30y^2$ since it has got one term it can not be a polynomial.

$30y^2+x$: it has got more than one term therefore, it is a polynomial.

$30y^2x$: again it has got just one term so it is not a polynomial.

$30y^2+x^{12}$: Since it has got more than one term, so again it is a polynomial.