Question

How to solve this showing all work ! Also explain why they aren’t polynomials if you can :)

Answer 1

Polynomials are linear combinations of positive integer powers. For example,

`x^(100)+30x^2-\sqrt 2\,x+21`

is a polynomial, but

`-x^(-1)-4x^\pi+x^(3/2)`

is not.

(In case you're unfamiliar with the term, a linear combination of two quantities is the sum of scaled versions of those quantities, e.g. a general linear combination of
`a` and
`b` is
`k_1a+k_2b`, where
`k_1,k_2` are any numbers.)

`8x^2-18\sqrt x+5x-3` is not a polynomial; the offending term is
`-18\sqrt x`, or
`-18x^(1/2)`.