(Q14) Give examples of polynomials p(x),g(x),q(x) and r(x) which satisfy the divison algorithm and
deg q(x)= deg r(x)

Answer

Let p(x)=x5+2x4+3x3+5x2+2

q(x)=x2+x+1, degree q(x)=2

Given degree q(x)= degree r(x)

On dividing x5+2x4+3x3+5x2+2 by x2+x+1, we get

3+2++
x2+x+1) 5+x4+x3+x2+
5+4+3
-   -   -
4+x3+x2+
4+3+2
-   -   -
3+x2+
3+2+
-   -   -
x2-+
2++
-   -   -
x2-x+

Here g(x)=3+2++

r(x)=x2-x+

degree of r(x)=

Degree of g(x) = Degree of r(x)