Question

Justify if the expression $\frac{\left(x-2\right)\left(x-4\right)}{7}$is polynomial.

Answer 1

Define polynomial:

An algebraic expression is polynomial if exponents of each of variable is a whole number, means a positive integer including zero.

The expression is given in the form, $\frac{\left(x-2\right)\left(x-4\right)}{7}$.

Simplify the expression:

$$\begin{gathered} \frac{\left(x-2\right)\left(x-4\right)}{7}=\frac{x^2-4x-2x+8}{7} \\ =\frac{x^2-6x+8}{7} \\ =\frac{1}{7}{x}^2-\frac{6}{7}x+\frac{8}{7} \end{gathered}$$

Thus, the simplified form of the given expression is $\frac{1}{7}{x}^2-\frac{6}{7}x+\frac{8}{7}$.

Here, the exponents of variable is whole number.

Thus, the given expression is polynomial.