Question

State whether the given algebraic expressions are polynomials? Justify.

(i) $y+\frac{1}{y}$ (ii) $2-5\sqrt{x}$ (iii) $x^2+7x+9$ (iv) $2m^{-2}+7m-5$ (v) 10

Answer 1

In an algebraic expression, if the powers of the variables are whole numbers then the algebraic expression is a polynomial.

(i)
$y+\frac{1}{y}=y+y^{-1}$

Here, one of the powers of y is −1, which is not a whole number. So, $y+\frac{1}{y}$ is not a polynomial.

(ii)
$2-5\sqrt{x}=2-5x^{\frac{1}{2}}$

Here, the power of x is $\frac{1}{2}$, which is not a whole number. So, $2-5\sqrt{x}$ is not a polynomial.

(iii)
$x^2+7x+9$

Here, the powers of the variable x are 2, 1 and 0, which are whole numbers. So, $x^2+7x+9$ is a polynomial.

(iv)
$2m^{-2}+7m-5$

Here, one of the powers of m is −2, which is not a whole number. So, $2m^{-2}+7m-5$ is not a polynomial.

(v)
10 = 10 × 1 = 10x⁰

Here, the power of x is 0, which is a whole numbers. So, 10 is a polynomial (or constant polynomial).