Question

give examples of polynomial p(x), g(x), q(x), r(x)which satisfy the division algorithm and (¡) deg p(x) = deg q(x) (¡¡) deg q (x) = deg r(x) (¡¡¡) deg r (x) =0​

Answer 1

We can write many such examples

(i) deg p(x) = deg q(x)

P(x) = x2, q(x) = x2, g(x) = 1, R(x) = 0

(ii) deg q(x) = deg r(x)

q(x) = x , R(x) = x , p(x) = x2 + x, g(x) = x2

(iii) deg r(x) = 0

q(x) = 1 , R(x) = 1 , p(x) = x+1, g(x) = x

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