5. Give examples of polynomials p(x), g(x), q(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
Solution (i)
Let p(x)=
g(x)=3
So, we can see in this example that deg p(x)=deg q(x)=2
Solution (ii)
Let p(x)=
And, g(x)=
We can see in this example that deg q(x)=deg r(x) =1
Solution (iii)
Let p(x)=
g(x) =
We can see in this example that deg r(x)=0
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