Question

Explain why the expression 9x^3+1/2x^2+3x^-1 is not a polynomial

Answer 1

The given expression can't be expressed in polynomial form. Hence, it is not a polynomial.

Explanation:

P(x,n) is a polynomial of nth degree if it is of the form,

P(x,n) =
`a_(0) + a_(1)x + a_(2)x^(2) + a_(3)x^(3) + ......... +a_(n)x^(n)`

where n is a finite positive integer and n ∈ N

and '
`a_(i)`'s are fixed but otherwise arbitrary constants ∀ i = 0(1)n .

Now, the given expression is,

`9x^(3) + \frac {1}{2x^(2)} + 3x^(-1)`

which doesn't fit in the above form. Hence, it is not a polynomial.