(Q6)Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following

p(x)=x4-3x2+4x+5, g(x)=x2+1-x

Given polynomials are

p(x)=x4-3x2+4x+5

g(x)=x2+1-x

Here, dividend already in the standard form and the divisor is not in the standard form. it can be written as x2-x+1

So, we have

2+-
x2-x+1) 4    -x2+x+
4 - 3 + 2
-   +   -
3-x2+x+
3-2+
-   +   -
-x2+x+
-x2+x-
+   -   +
+

The quotient is 2+x- and the remainder is +