Question

Is (y+2/y) polynomial in one variable? Please state reason for your answer.
Thank you.​

Answer 1

Answer:

It is not a polynomial in one variable.

(y+2)/y is (y+2)×y to the power (-1).So, it is not a polynomial.

Definition of polynomial:A polynomial is an algebraic expression in which the variables have positive integral powers.

Answer 2

Answer:

Yes, $\left(y+\frac{2}{y}\right)$ is a polynomial in one variable.

Step-by-step explanation:

The polynomial that consists of only one variable is termed the polynomial in one variable.

Polynomial of one variable can be of any degree.

For example: $ax+b=0$, $ax^2+bx+c=0$ and many more.

where $a$, $b$ and $c$ are constants.

The general form of one variable polynomial is,

$a_nx^n+a_{n-1}x^{n-1}+.\ .\ .\ +a_1x^1+a_0$, where $a_i's$ are the constants.

Consider the given polynomial as follows:

$y+\frac{2}{y}=0$

Simplify the equation as follows:

$\frac{y^2+2}{y} =0$

Multiply both the sides by variable $y$ as follows:

⇒ $y\left(\frac{y^2+2}{y}\right) =y\times0$

⇒ $y^2+2=0$ . . . . . (2)

Notice that equation (2) has only one variable, i.e. $y$.

Therefore, the polynomial $\left(y+\frac{2}{y}\right)$ is one variable polynomial.

#SPJ2