(Q15) Give examples of polynomials p(x),g(x),q(x) and r(x) which satisfy the divison algorithm and
deg r(x)= 0

Answer

Let p(x)=2x4+8x3+6x2+4x+12

r(x)=2

Here, degree r(x)=0

On dividing 2x4+8x3+6x2+4x+12 by 2, we get

4+x3+x2+x+
2) x4+x3+x2+x+
x4
-
x3+x2+x+
x3
-
x2+x+
x2
-
x+
x
-
-

Here ,g(x)=4+x3+x2+x+ and r(x)=

so degree of r(x)=