Question

State, giving the reason, whether the following expressions are polynomials or not.

(1) b² − 25
(2) $y^{\frac{1}{2}}+18-5y$
(3) $\frac{7}{m}-2$

Answer 1

(1) The powers 2 and 0 of the variable b in b² − 25 are whole numbers.
Hence, b² − 25 is a polynomial.

(2) In the expression $y^{\frac{1}{2}}+18-5y$, the index $\frac{1}{2}$ is not a whole number.
Hence, this expression is not a polynomial.

(3) In the expression $\frac{7}{m}-2\left(i.e.7m^{-1}-2\right)$, the index −1 is not a whole number.
Hence, this expression is not a polynomial.