Question

What are the answers to the attachment and how did you get that answer

Answer 1

A Polynomials are sums of terms of the form

`k.x^n`

where k is any number and n is a positive integer. Hence n must be a positive whole number

`\begin{gathered} x^2+1 \\ is\text{ a polynomial } \\ \text{This is because the exponent or power (2) is a positive whole number } \end{gathered}`
`\begin{gathered} x^{(1)/(2)}+1 \\ is\text{ not a polynomial } \\ \text{This is because polynomial cannot contain a fractional exponent or } \\ \text{power. }(1)/(2)\text{ is a fraction } \\ \text{hence }x^{(1)/(2)}+1\text{ is not a polynomial } \end{gathered}`
`\begin{gathered} (x)/(3) \\ is\text{ a polynomial } \\ \text{This is because }x\text{ can also be written as }x^1 \\ so,\text{ the power or exponent (1) is a whole number. } \\ \text{Hence }(x)/(3)\text{ is a polynomial } \end{gathered}`