Question

Which of the following expression are polynomial? Justify your answer:

`((x - 2)(x - 4))/x`

Answer 1

`((x - 2)(x - 4))/x = (x^2 - 4x - 2x + 8)/x`

= `(x^2 - 6x + 8)/x`

= `x - 6 + 8/x`

= x – 6 + 8x^–1

Here, the power of x = –1, which is not a whole number, but a negative number.

Hence, `((x - 2)(x - 4))/x` is not a polynomial.