Question

$\frac{(x - 2)(x - 4)}{x}$
is the above mentioned expression a polynomial or not. justify your answer​

Answer 1

Yes it is a polynomial. Since the highest exponent of x is greater than 2 then the expression gives a polynomial function.20-May-2020

Answer 2

$\frac{( x- 2)(x - 4)}{x}$

$\implies \frac{ {x}^{2} - 4x - 2x + 8}{x}$

$\implies \frac{ {x}^{2} - 6x + 8}{x}$

$\implies \frac{ {x}^{2} }{x} - \frac{6x}{x} + \frac{8}{x}$

$\implies {x} - 6 + 8 {x}^{ - 1}$

Since the power of $x$ is negative

we can conclude that its Not a Polynomial.

(For an expression to be a Polynomial power must be non-negative)

HOPE IT HELPS!!