(Q7) Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following

p(x)=x4-5x+6, g(x)=2-x2

Given polynomials are

p(x)=x4-5x+6

g(x)=2-x2

Here, the dividend is already in the standard form and the divisor is not in the standard from.it can be written as x2+2

So, we have

-2-
-x2+2) 4-x+
4-x2
-   +
x2-x+
x2    -
-x+

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