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Give example of polynomials p(x),g(x),q(...

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

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To solve the problem, we need to provide examples of polynomials \( p(x) \), \( g(x) \), \( q(x) \), and \( r(x) \) that satisfy the conditions of the division algorithm. The division algorithm states that for any polynomials \( p(x) \) and \( g(x) \) (where \( g(x) \) is not zero), 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 either \( r(x) = 0 \) or the degree of \( r(x) \) is less than the degree of \( g(x) \). ...
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