Give examples of polynomials p(x), g(x), g(x) and r(x), which satisfy the division algorithm and
(i) `"deg p(x)=deg q(x)"`
(ii) `"deg q(x)=deg r(x)"`
(iii) `"deg r(x)=0"`

Explanation

To solve the problem, we need to provide examples of polynomials \( p(x) \), \( g(x) \), \( q(x) \), and \( r(x) \) that satisfy the conditions given in the question. We will use the polynomial division algorithm which states that for any two polynomials \( p(x) \) and \( g(x) \) (where \( g(x) \neq 0 \)), there exist unique polynomials \( q(x) \) (the quotient) and \( r(x) \) (the remainder) such that:

\[ p(x) = g(x) \cdot q(x) + r(x) \]

where the degree of \( r(x) \) is less than the degree of \( g(x) \).

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